From MAILER-DAEMON Fri Nov 7 15:43:16 2003 Date: 07 Nov 2003 15:43:16 -0400 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1068234196@mta.ca> X-IMAP: 1068234141 0000000059 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Wed May 7 14:19:43 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:19:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DSZK-0007R4-00 for categories-list@mta.ca; Wed, 07 May 2003 14:19:02 -0300 Message-ID: <3EB0F99C.9060105@cs.bham.ac.uk> Date: Thu, 01 May 2003 11:40:28 +0100 From: Steve Vickers User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.3) Gecko/20030312 X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Zariski spectra for rings with topology Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 If R is a ring (commutative, with 1), there is a certain sense in which the structure sheaf, a local homeomorphism E -> Spec(R) (making the Zariski spectrum a local ringed space) is the free local ring over R. Can this be made to work more generally for localic rings R? (Other than in trivial ways, by taking the set of points of R.) Or for particular classes of localic rings (e.g. compact regular)? Is there a Zariski spectrum? Presumably the analogue of the structure sheaf would not be a local homeomorphism any more. Steve Vickers. From rrosebru@mta.ca Wed May 7 14:22:25 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:22:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DScS-00001S-00 for categories-list@mta.ca; Wed, 07 May 2003 14:22:16 -0300 Date: Fri, 2 May 2003 08:24:21 -0500 (EST) From: "NASSLLI'03 Bloomington, Indiana" X-Sender: nasslli@lear.ucs.indiana.edu Reply-To: "NASSLLI'03 Bloomington, Indiana" To: Undisclosed recipients: ; Subject: categories: EXTENDED EARLY REGISTRATION for NASSLLI 2003 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 2 EARLY REGISTRATION EXTENDED to May 10 for NASSLLI'03, MoL 8, and TARK IX NASSLLI'03, June 17-21 North American Summer School in Logic, Language and Information www.indiana.edu/~nasslli NASSLLI is a week-long summer school featuring courses on many topics of interest to students and researchers. The main focus is on the interface between linguistics, logic, and computation, broadly conceived, and on related fields. NASSLLI includes twelve courses a student session, invited evening speakers, and lively interaction. NASSLLI is co-located this year with two conferences: MoL 8, June 20-22 Mathematics of Language http://www.cis.upenn.edu/~ircs/mol/mol8program.pdf MoL offers a platform for research on mathematical linguistics and the mathematical study of natural languages. TARK IX, June 20-22 Theoretical Aspects of Rationality and Knowledge http://www.tark.org/cfp03.html TARK brings together researchers from a wide variety of fields in order to further our understanding of interdisciplinary issues involving reasoning about rationality and knowledge. ACT NOW for early registration! >>> To register for any of these, please see www.indiana.edu/~nasslli <<< When registering, please disregard the May 1st deadline, you will be charged only the early registration fee. From rrosebru@mta.ca Wed May 7 14:24:53 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:24:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DSed-0000GH-00 for categories-list@mta.ca; Wed, 07 May 2003 14:24:31 -0300 Date: Mon, 5 May 2003 13:46:43 -0400 (EDT) From: Oswald Wyler To: categories@mta.ca Subject: categories: Query Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 3 For every set Z, there is a self-adjoint contravariant functor Q=ENS(--,Z), with unit/counit h:Id-->Q^op Q given by (h_X)(x)(f)=f(x). Let Q-alg denote the category of algebras for the monad induced by this self-adjunction. If Z is not empty or a singleton, then the comparison functor ENS^op-->Q-alg is an equivalence by results of M. Sobral. If Z has two members, then Q-alg is isomorphic to CaBool, the category of complete atomic Boolean algebras. What is known about Q-alg if Z has more than two members (beyond the fact that Q-alg and CaBool are equivalent)? From rrosebru@mta.ca Wed May 7 14:29:34 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:29:34 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DSjL-0000iQ-00 for categories-list@mta.ca; Wed, 07 May 2003 14:29:23 -0300 X-Sender: grandis@pop4.dima.unige.it Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 6 May 2003 11:45:52 +0200 To: categories@mta.ca From: grandis@dima.unige.it (Marco Grandis) Subject: categories: Preprint: Directed combinatorial homology and noncommutative tori X-OriginalArrivalTime: 06 May 2003 09:38:35.0718 (UTC) FILETIME=[43FC2E60:01C313B3] Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 4 The following preprint is available: M. Grandis Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology), Dip. Mat. Univ. Genova, Preprint 480 (May 2003), 29 p. Abstract. This is a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing *directed spaces*, breaking the intrinsic symmetries of topological spaces. Cubical sets have a *directed homology*, consisting of preordered abelian groups where the positive cone comes from the structural cubes. But cubical sets can also express topological facts missed by ordinary topology. This happens, for instance, in the study of group actions or foliations, where a topologically-trivial quotient (the orbit set or the set of leaves) can be enriched with a natural cubical structure whose directed cohomology agrees with Connes' analysis in noncommutative geometry. Thus, cubical sets can provide a sort of 'noncommutative topology', without the metric information of C*-algebras. MSC: 55U10, 55Nxx, 81R60. Keywords: Cubical sets, combinatorial homology, noncommutative spaces, directed algebraic topology. Available in .pdf and .ps at: http://www.dima.unige.it/~grandis/Bsy.pdf http://www.dima.unige.it/~grandis/Bsy.ps _____ Marco Grandis Dipartimento di Matematica Universita` di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ From rrosebru@mta.ca Thu May 8 13:25:52 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 May 2003 13:25:52 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DoCJ-0003rf-00 for categories-list@mta.ca; Thu, 08 May 2003 13:24:43 -0300 Message-Id: <200305071855.LAA22674@coraki.Stanford.EDU> X-Mailer: exmh version 2.1.1 10/15/1999 To: categories@mta.ca Subject: categories: re: Query (Q-algebras) In-Reply-To: Message from Oswald Wyler of "Mon, 05 May 2003 13:46:43 EDT." Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Wed, 07 May 2003 11:55:08 -0700 From: Vaughan Pratt X-Scanner: exiscan for exim4 *19DUBp-0003yO-00*288I3uw4n6c* Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 5 The operations of Q-alg are the functions between the powers of the set Z, forming the (Lawvere) theory T of Q-algebras, which are product-preserving functors from T to Set. (So if Z is 3 then there are 27 = 3^3 "Boolean" operations in place of the familiar 4 = 2^2.) With all powers Q-algebras are equivalent to CABAs, with only finite powers and finite-product-preserving functors they are equivalent to Boolean algebras. A natural next question would be, what is obtained when T is taken to be Set itself, in each of the cases when the functors T->Set are required to preserve all limits, and just the discrete ones? Vaughan Pratt >From: Oswald Wyler >For every set Z, there is a self-adjoint contravariant functor Q=ENS(--,Z), >with unit/counit h:Id-->Q^op Q given by (h_X)(x)(f)=f(x). Let Q-alg denote >the category of algebras for the monad induced by this self-adjunction. >If Z is not empty or a singleton, then the comparison functor ENS^op-->Q-alg >is an equivalence by results of M. Sobral. If Z has two members, then Q-alg >is isomorphic to CaBool, the category of complete atomic Boolean algebras. >What is known about Q-alg if Z has more than two members (beyond the fact >that Q-alg and CaBool are equivalent)? From rrosebru@mta.ca Thu May 8 13:27:19 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 May 2003 13:27:19 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DoEL-00047K-00 for categories-list@mta.ca; Thu, 08 May 2003 13:26:49 -0300 Date: Thu, 8 May 2003 06:05:11 +0200 (CEST) From: Tom LEINSTER To: categories@mta.ca Subject: categories: Book: Higher Operads, Higher Categories Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset="US-ASCII" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 6 Dear Colleagues, I'm very happy to announce the availability of my book, "Higher Operads, Higher Categories". It is available electronically now, and will appear in traditional print form later in the year. The electronic version is at http://arxiv.org/abs/math.CT/0305049 and the nice bound version is Tom Leinster, Higher Operads, Higher Categories, London Mathematical Society Lecture Notes Series, Cambridge University Press, ISBN 0-521-53215-9. Details of the latter will appear at the CUP website (www.cambridge.org), and it can also be pre-ordered from the usual on-line book stores. The existence of the electronic version is by arrangement with CUP, more on which below; first, some mathematical details. SUMMARY Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. This is the first book on the subject and lays its foundations. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. Many examples are given throughout. There is also an introductory chapter motivating the subject for topologists. CONTENTS Diagram of interdependence Acknowledgements Introduction Motivation for topologists I Background 1 Classical categorical structures 2 Classical operads and multicategories 3 Notions of monoidal category II Operads 4 Generalized operads and multicategories: basics 5 Example: fc-multicategories 6 Generalized operads and multicategories: further theory 7 Opetopes III n-Categories 8 Globular operads 9 A definition of weak n-category 10 Other definitions of weak n-category Appendices A Symmetric structures B Coherence for monoidal categories C Special cartesian monads D Free multicategories E Definitions of tree F Free strict n-categories G Initial operad-with-contraction Bibliography Glossary of notation Index The arrangement with CUP is that I can post a "preprint" version of the book on the archive now, and then one year after the book has been published in traditional form, I can update the archive version to agree with it. All I've done in return is to give up my royalties (10% of the profit; there goes my fortune). This is something of an experiment on CUP's part: they initially said that it would hurt their sales too much to have a free electronic version available, then I tried to persuade them that it might actually help sales, not hurt them, because of the extra exposure it would get. There's also the consideration that a 400-page printout is unwieldy and the book is low-price, so the incentive for readers to buy is quite high. In any case, I think that CUP deserve a great deal of credit for being willing to try this, and I'd be pleased if those who can afford to bought a copy rather than just using the printout; this would reflect the goodwill and perhaps encourage CUP to extend this arrangement to other authors. It'll be about 30 pounds (45 euros or US$) - and as I said, I make no money from this. Tom From rrosebru@mta.ca Thu May 8 16:35:43 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 May 2003 16:35:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Dr8U-0005Dy-00 for categories-list@mta.ca; Thu, 08 May 2003 16:32:58 -0300 Date: Wed, 7 May 2003 10:08:40 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Jon Beck's thesis Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 7 I need some volunteers who are willing to type parts of Jon Beck's thesis that we are planning to put into the TAC reprint series. I will do all the diagrams and also do part of the rest, but if we had ten volunteers, it would probably be less than a day's work for each of them. The thesis is about 125 pages. Michael From rrosebru@mta.ca Thu May 8 16:53:33 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 May 2003 16:53:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DrRz-00074B-00 for categories-list@mta.ca; Thu, 08 May 2003 16:53:07 -0300 To: categories@mta.ca Subject: categories: Re: Query (Q-algebras) In-Reply-To: Message from Vaughan Pratt of "Wed, 07 May 2003 11:55:08 PDT." <200305071855.LAA22674@coraki.Stanford.EDU> Date: Thu, 08 May 2003 12:05:50 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 >(So if Z is 3 then there are 27 = 3^3 "Boolean" operations in place of >the familiar 4 = 2^2.) There should have been a "unary" in there of course. Another question about these Q-algebras that Oswald Wyler was asking about: what is a necessary and sufficient condition for a complete basis for finitary Q-algebras (the theory of Boolean algebras rather than CABAs) having any given Z? For Z = 2 one answer (at least for the version of the problem which only considers nonzeroary operations) is that for each of the following properties the basis must contain a counterexample to that property. Necessity follows because each property is preserved under composition; sufficiency takes more work. * selfdual (e.g. xy+yz+zx = (x+y)(y+z)(z+x)) * monotone * affine (expressible as the XOR of its arguments, optionally plus 1) * strict (maps the all-zeros input to zero) * costrict (maps the all-ones input to one) (NAND violates all five at once.) Is there a fixed number of such properties that works for all finite cardinalities of Z, or must the number of properties of this kind grow with Z? Vaughan Pratt From rrosebru@mta.ca Fri May 9 11:50:53 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 May 2003 11:50:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19E9Az-0006M8-00 for categories-list@mta.ca; Fri, 09 May 2003 11:48:45 -0300 Date: Fri, 9 May 2003 11:41:25 -0300 (ADT) From: Bob Rosebrugh To: categories Subject: categories: Re: Jon Beck's thesis (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 9 [Note from moderator: Mike Barr reports over 15 volunteers already, thanks to all, that should be sufficient.] ---------- Forwarded message ---------- Date: Wed, 7 May 2003 10:08:40 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Jon Beck's thesis I need some volunteers who are willing to type parts of Jon Beck's thesis that we are planning to put into the TAC reprint series. I will do all the diagrams and also do part of the rest, but if we had ten volunteers, it would probably be less than a day's work for each of them. The thesis is about 125 pages. Michael From rrosebru@mta.ca Fri May 9 12:49:35 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 May 2003 12:49:35 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19EA3l-000530-00 for categories-list@mta.ca; Fri, 09 May 2003 12:45:21 -0300 From: "Ernie Manes" To: References: Subject: categories: Re: Query (Q-algebras) Date: Fri, 9 May 2003 07:24:35 -0400 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 Hi Vaughan, Regarding these and similar questions, I suggest looking at the following two gems: A. L. Foster, Gerneralized "Boolean" theory of universal algebras, Part II. Identities and subdirect sums of functionally complete algebras, Math. Zeit. 59, 1953, 191-199. T.-K. Hu, Stone duality for primal algebra theory, Math. Zeit. 110, 1060, 180-198. Ernie Manes ----- Original Message ----- From: "Vaughan Pratt" To: Sent: Thursday, May 08, 2003 3:05 PM Subject: categories: Re: Query (Q-algebras) > > > >(So if Z is 3 then there are 27 = 3^3 "Boolean" operations in place of > >the familiar 4 = 2^2.) > > There should have been a "unary" in there of course. > > Another question about these Q-algebras that Oswald Wyler was asking > about: what is a necessary and sufficient condition for a complete basis > for finitary Q-algebras (the theory of Boolean algebras rather than CABAs) > having any given Z? For Z = 2 one answer (at least for the version of the > problem which only considers nonzeroary operations) is that for each of the > following properties the basis must contain a counterexample to that property. > Necessity follows because each property is preserved under composition; > sufficiency takes more work. > > * selfdual (e.g. xy+yz+zx = (x+y)(y+z)(z+x)) > * monotone > * affine (expressible as the XOR of its arguments, optionally plus 1) > * strict (maps the all-zeros input to zero) > * costrict (maps the all-ones input to one) > > (NAND violates all five at once.) Is there a fixed number of such properties > that works for all finite cardinalities of Z, or must the number of properties > of this kind grow with Z? > > Vaughan Pratt > > From rrosebru@mta.ca Fri May 9 12:49:45 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 May 2003 12:49:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19EA4e-00055n-00 for categories-list@mta.ca; Fri, 09 May 2003 12:46:16 -0300 Date: Fri, 9 May 2003 07:36:24 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Enough already (Beck's thesis) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 11 I am gratified to announce that I already have a dozen or more volunteers and that would seem to be enough. More will increase the coordination problem, of which I have begun thinking might not be trivial. Thanks again to all the willing volunteers. Michael From rrosebru@mta.ca Sun May 11 12:56:03 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 11 May 2003 12:56:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Et6Q-0004Xd-00 for categories-list@mta.ca; Sun, 11 May 2003 12:51:06 -0300 To: categories@mta.ca Subject: categories: Dualization monads on sets Date: Sat, 10 May 2003 20:59:07 -0400 From: wlawvere@buffalo.edu Message-ID: <1052614747.3ebda05b1421e@mail2.buffalo.edu> X-Mailer: University at Buffalo WebMail Cyrusoft SilkyMail v1.1.10 24-January-2003 MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 As discussed his week by Oswald Wyler, Vaughan Pratt, and Ernie Manes, the opposite of the category of small sets is equivalent to the algebras over the monad T obtained by dualizing into Z for Z>1 ; there is really no difference which Z is used. But that changes if we consider a truncation of T, i.e., the part supported by arity I for some I (the truncated monad has value at X equal to the union of the images of T(I)--> T(X) over all I-->X). There is still the possibility that some subcategory of sets will be full in the opposite of the category of algebras. For example, as Vaughan points out, if Z=3, I=1, at least the finite sets can be so captured. An important way to capture all small sets is to take Z=2 and I= countable (Ulam) or Z=countable and I=1 (Isbell in 1960 showed that these are equivalent). Taking unary operations (I=1) is always possible by enlarging Z. (For some reason Ulam spoke of measures, which is really quite misleading because measures are additive but here the condition that they be multiplicative is at least as important; likewise the set -theorists' terminology "measurable" (for sets too big to be captured) is misleading because "to be capturable" is intuitively to be measurable by procedures valued in Z.) I advocate that an additional axiom on small sets is that all such monads (Z infinite, I=1) should be the identity, because all known constructions of geometry and analysis preserve capturability and moreover all mathematical situations where one can reasonably expect a space/quantity duality are spoiled without this axiom on the underlying discrete sets. It is well known that the negation of the axiom, as applied to all sets, implies its consistency. Recognizing a category of small sets, so defined, as an ordinary object in the cartesian-closed category of categories of course in no way prevents the consideration of possible much larger sets or categories in the same system, no more than does recognizing the category of finite sets. From rrosebru@mta.ca Tue May 13 16:31:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2003 16:31:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19FfS9-0003Fy-00 for categories-list@mta.ca; Tue, 13 May 2003 16:28:45 -0300 Message-Id: <200305130744.h4D7iFC14111@math.u-strasbg.fr> Date: Tue, 13 May 2003 09:44:15 +0200 (MEST) From: Philippe Gaucher Reply-To: Philippe Gaucher Subject: categories: preprint : A long exact sequence for the branching homology To: categories@mta.ca X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.2 SunOS 5.8 sun4u sparc Content-Type: text X-Sun-Text-Type: ascii X-Antivirus: scanned by sophos at u-strasbg.fr Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 13 Author : Philippe Gaucher Title : A long exact sequence for the branching homology Abstract : A function complex is introduced on the category of flows so that the model category of flows becomes a simplicial model category. This allows us to show that the homotopy branching space of the cone of a morphism of flows is homotopy equivalent to the cone of its image by the homotopy branching space functor. The crux of the proof is that the homotopy branching space of the terminal flow is contractible. We then easily deduce a long exact sequence for the branching homology of a flow. Url : http://www-irma.u-strasbg.fr/~gaucher/ or Arxiv : math.AT/0305169 From rrosebru@mta.ca Tue May 13 16:31:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2003 16:31:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19FfQi-0003AE-00 for categories-list@mta.ca; Tue, 13 May 2003 16:27:16 -0300 Mime-Version: 1.0 X-Sender: kimail@Janeway.Inf.TU-Dresden.DE Message-Id: Date: Mon, 12 May 2003 19:58:55 +0200 To: categories@mta.ca From: "Proof Theory, Computation and Complexity" Subject: categories: Proof Theory, Computation and Complexity Summer School and Workshop Content-Type: text/plain; charset="iso-8859-1" ; format="flowed" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 14 Summer School and Workshop on Proof Theory, Computation and Complexity =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Technische Universitaet Dresden June 23-July 4, 2003 Call for Participation ---------------------- We plan the following courses and workshop for graduate students and researchers. Like for last year's events on `Proof Theory and Computation=B4 (Dresden) and `Proof, Computation, Complexity=B4 (Tuebingen), we aim at a meeting where people have plenty of time to exchange ideas. The summer school consists of eight advanced courses; the workshop is integral part of the school and takes place in the last two days. We ask for a participation fee of 100 EUR. A limited number of grants covering all expenses is available. Registration is requested before May 25, 2003; please send an email to PTEvent@Janeway.Inf.TU-Dresden.DE, making sure you include a very brief bio (5-10 lines) stating your experience, interests, home page, etc. We will select applicants in case of excessive demand. We will provide assistance in finding an accommodation in Dresden. Week 1, June 23-27: courses on Denotational Semantics of Lambda Calculi Achim Jung (Birmingham, UK) Semantics and Cut-elimination for Church's (Intuitionistic) Theory of Types, with Applications to Higher-order Logic Programming Jim Lipton (Wesleyan, USA) Five Lectures on Proof-Analysis Sara Negri (University of Helsinki and Academy of Finland) Mass Problems Stephen Simpson (Penn State, USA) Week 2 June 30-July 2: courses on Dependent Type Theories Peter Aczel (Manchester, UK) Term-rewriting and Termination in Proof Theory Roy Dyckhoff (St Andrews, Scotland) Proof Theory with Deep Inference Alessio Guglielmi (Dresden, Germany) Natural Deduction: Some Recent Developments Jan von Plato (Helsinki, Finland) July 3-4: workshop Please consult the workshop web page: . Venue ----- Dresden, on the river Elbe, is one of the most important art cities of Germany. You can find world-class museums and wonderful architecture and surroundings. We will organize trips and social events. Organization ------------ This event is organized by Paola Bruscoli, Birgit Elbl, Bertram =46ronh=F6fer, Alessio Guglielmi, Reinhard Kahle, Charles Stewart and the AI Institute at TU Dresden, and sponsored by Deutscher Akademischer Austausch Dienst, IQN (Rational mobile agents and systems of agents), Graduiertenkolleg 334 (Specification of discrete processes and systems of processes by operational models and logics) and Consolato Generale d'Italia - Lipsia/Italienisches Generalkonsulat in Leipzig. Please distribute this message broadly. From rrosebru@mta.ca Tue May 13 16:40:54 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2003 16:40:54 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19FfdW-0004NG-00 for categories-list@mta.ca; Tue, 13 May 2003 16:40:30 -0300 Message-ID: <3EBF88C9.24BCEFD4@bangor.ac.uk> Date: Mon, 12 May 2003 12:43:05 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.79 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: "categories@mta.ca" Subject: categories: Towards non commutative algebraic topology Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to advertise the term `Non commutative algebraic topology' and to give a quick view of background, ideas, and some calculations, in the application of some non commutative methods to this area. 25 pages, in transparency format; printing the pdf file at 4 pages per A4 sheet is readable. Available as: math.AT/0305165 http://www.bangor.ac.uk/~mas010/noncommut-at.pdf Ronnie Brown School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Centre for the Popularisation of Mathematics: http://www.cpm.informatics.bangor.ac.uk/ (reorganised site with new sculpture animations) From rrosebru@mta.ca Tue May 13 16:41:29 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2003 16:41:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19FfeL-0004Ri-00 for categories-list@mta.ca; Tue, 13 May 2003 16:41:21 -0300 content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Subject: categories: Book announcement X-MimeOLE: Produced By Microsoft Exchange V6.0.6249.0 Date: Tue, 13 May 2003 09:50:47 +0200 From: "boerger" To: Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 Egon Boerger and Robert Staerk Abstract State Machines. A Method for High-Level System Design = and Analysis=20 X+438p., Hardcover, EUR 49,95 Springer-Verlag 2003, ISBN 3-540-00702-4 =20 The systems engineering method proposed in this book, which is based on Abstract State Machines (ASMs), guides the development of software and embedded hardware-software systems seamlessly from requirements capture to actual implementation and documentation. Within a single conceptual framework it covers design, verification by reasoning techniques, and validation by simulation and testing. ASMs improve current industrial practice by using accurate high-level modeling and by linking the descriptions at the successive stages of system development in an organic and efficiently maintainable chain of rigorous and coherent system models at stepwise-refined abstraction levels. =20 This book combines the features of a textbook and a handbook. Researchers will find here the most comprehensive description of ASMs available today and professionals will use it as a "modeling handbook for the working software engineer." As a textbook it supports self-study or it can form the basis of a lecture course. The book is complemented by a CD containing the whole book text, additional course material, solutions to exercises, and additional examples. Lecture notes and additional material are freely available=20 at the AsmBook website=20 http://www.di.unipi.it/AsmBook/ Contents: 1. Introduction 2. ASM Design and Analysis Method 3. Basic ASMs (Ground Model and Refinement Method) 4. Structured ASMs (Composition Techniques) 5. Synchronous Multi-Agent ASMs 6. Asynchronous Multi-Agent ASMs 7. Universal Specification and Computation Model 8. Tool Support for ASMs 9. History and Survey of ASM Research - References Please order from our web site www.springer.de, from your local bookseller, or from Springer directly. Orders can also be placed by sending an email to orders@springer.de . Shipping charges within Europe are EUR 5 per book, plus EUR 1.50 for each additional book; except Germany, Austria, Switzerland EUR 2.50 per order. Springer GmbH & Co. KG=20 Auslieferungs-Gesellschaft Order Processing=20 Haberstra=DFe 7 69126 Heidelberg Germany FAX: +49-6221-345-229 See also http://www.amazon.de/exec/obidos/ASIN/3540007024/ http://www.amazon.co.uk/exec/obidos/ASIN/3540007024/ http://www.amazon.com/exec/obidos/ASIN/3540007024/ From rrosebru@mta.ca Wed May 14 16:42:37 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 May 2003 16:42:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19G22t-00017N-00 for categories-list@mta.ca; Wed, 14 May 2003 16:36:11 -0300 Date: Tue, 13 May 2003 23:37:44 -0400 (EDT) From: Amy Felty To: Subject: categories: LICS 2003 - Call for Participation Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 *** NOTE: EARLY REGISTRATION AND ACCOMMODATION DEADLINE IS MAY 20, 2003 *** Eighteenth Annual IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS 2003) June 22 - 25, 2003, Ottawa, Canada http://www.dcs.ed.ac.uk/home/als/lics/lics03/ CALL FOR PARTICIPATION The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. The conference is intended to emphasize the relevance of logic to computer science. The program of LICS 2003 features 4 invited talks, 2 invited tutorials, 34 contributed papers, and 14 short presentations. Invited Talks: - Erich Graedel (RWTH Aachen): "Will deflation lead to depletion? On non-monotone fixed point inductions" - John Harrison (Intel Corp.): "Formal verification at Intel" - Marta Kwiatkowska (U. Birmingham) "Model checking for probability and time: from theory to practice" - John McCarthy (Stanford U.) "Advice about nonmonotonic reasoning in AI" Invited Tutorials: - Martin Abadi (UC Santa Cruz): "Logic in Access Control" - Benjamin Pierce (U. Pennsylvania) "Types and Programming Languages: The Next Generation" The full program of LICS 2003 is available on the conference website http://www.dcs.ed.ac.uk/home/als/lics/lics03/ Affiliated Workshops: As in previous years, there will be a number of workshops affiliated with LICS 2003: - June 21: Probability in AI Organizer: Doina Precup - June 21: Typical Case Complexity and Phase Transitions, Organizers: Evangelos Kranakis and Lefteris Kirousis - June 26: Logic and Computational Linguistics Organizers: Gerald Penn and Leonid Libkin - June 26: Causality in Computer Science and Physics Organizer: Prakash Panangaden - June 26-27: Foundations of Computer Security Organizer: Iliano Cervesato - June 26-27 Implicit Computational Complexity Program chair: Anuj Dawar Pre-LICS Summer School: The Fields Institute Summer School on Logic and Foundations of Computation will be held at the University of Ottawa, June 2-20, 2003 For information, see the summer school web site at: http://www.mathstat.uottawa.ca/lfc/fields2003/ Registration: LICS 2003 registration and conference information is now available on the LICS 2003 website or directly at: http://www.mathstat.uottawa.ca/lfc/lics2003/ The DEADLINE FOR EARLY REGISTRATION is Tuesday, May 20, 2003. Web registration ends June 12. After that, registration will be on-site at the conference location. From rrosebru@mta.ca Thu May 15 15:02:17 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 15 May 2003 15:02:17 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19GN1Q-0003Cr-00 for categories-list@mta.ca; Thu, 15 May 2003 15:00:04 -0300 Date: Wed, 14 May 2003 08:08:36 -0500 (EST) From: "NASSLLI'03 Bloomington, Indiana" X-Sender: nasslli@lear.ucs.indiana.edu To: Undisclosed recipients: ; Subject: categories: NASSLLI funding available Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 18 Important notice: financial assistance NASSLLI has recently received some funds that we'd like to use to support student attendance. If you are interested, please send us a letter saying that you are planning to attend NASSLLI, what your field of study is and how far along you are, and how much of the expenses for NASSLLI you are paying yourself. Please also ask your adivsor, or a faculty person who knows you well, to also send us a short note. We expect to have a reasonable number of $100 registration reductions available. If you already registered for NASSLLI, you still can apply for the reduction. Please send all correspondence to nasslli@indiana.edu. More information at http://www.indiana.edu/~nasslli From rrosebru@mta.ca Fri May 16 16:16:01 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 May 2003 16:16:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Gkcm-0002LE-00 for categories-list@mta.ca; Fri, 16 May 2003 16:12:12 -0300 Message-Id: <200305160038.h4G0cQ7A013177@imgw1.cpsc.ucalgary.ca> Date: Thu, 15 May 2003 18:38:26 -0600 (MDT) From: Robin Cockett Reply-To: robin@cpsc.ucalgary.ca Subject: categories: FMCS '03: preliminary program and call for participation To: categories@mta.ca In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 20 FOUNDATIONAL METHODS IN COMPUTER SCIENCE (FMCS 2003) May 30 - June 1, Ottawa, Canada We are happy to announce the preliminary schedule for FMCS 2003 (see below). For Local Information Contact: Rick Blute Dept. of Mathematics & Statistics, University Ottawa, 613-562-5800, ext. 3535. The FMCS webpage (in process of being updated) is: http://www.mathstat.uottawa.ca/lfc/fmcs2003/ The Fields Institute Summer Program continues from the FMCS theme for the month of June, culminating in Fields Workshops (June 15--June 20), and LICS & workshops (June 20-27). For more information these are the webpages: http://www.mathstat.uottawa.ca/lfc/fields2003/ http://www.dcs.ed.ac.uk/home/als/lics/lics03/ ======================================================================= Preliminary Schedule - FMCS Location: * Day 1 talks (Friday, May 30th): Lamoureux 121. * Day 2, 3 talks: To be held at the Department of Mathematics and Statistics, 585 King Edward St., Room B5. Schedule * Day 1 - Friday, May 30th - Tutorials (in Lamoureux 121) - 9:30-11. Rick Blute: "Nuclear ideals" - 11-11:30. Break - 11:30-1. Robert Seely: "Double negation coherence" - 1-2:30. Lunch. - 2:30-4. Michael Barr: "Introduction to $*$-autonomous categories and the Chu construction" - 4-4:30. Break - 4:30-6. Dominic Hughes: "Extending Proof nets to products and sums" * Day 2 - Saturday, May 31st - Tutorial, contributed talks and invited lectures - 9-10:30. Ernie Manes: "Cockett-Lack restriction: Categories, semigroups and topology" - 10:30-11. Break. - 11-11:40. Phil Mulry: TBA - 11:40-12:20. Varmo Vene: "The dual of substitution is redecoration" - 12:30-2. Lunch - 2-2:40. Bob Rosebrugh: "Partial information and the sketch data model" - 2:45-3:15 Jeff Egger: "Adherence Spaces" - 3:20-3:50. Craig Pastro: "$\Sigma/\Pi$-polycategories" - 3:50-4:20. Break - 4:20-5:00. Dorette Pronk: ``Nuclear ideals and Segal's definition of conformal field theory''. - 5:05-5:45. John MacDonald: ``Parameters and Kleisli Structures'' * Day 3-Sunday, June 1st - 9-9:40. Noson Yanofsky: "On paradoxes, incompleteness and fixed points" - 9:45-10:15. Dana Harrington: "Coherence for uniqueness types" - 10:20-10:50. Brett Giles: An implementation of Selinger's quantum programming language" - 10:50-11:20. Break. - 11:20-11:50. Guy Beaulieu: Probabilistic Pi-Calculi - 11:55-12:35. Claudio Hermida: "Saturated partial algebras" - 12:35-2. Lunch - 2-2:40. Jonathon Funk: "Rough Sets and Topos Theory" - 2:45-3:25. Robin Cockett: "Circular proofs: once more round the block" - 3:30-4:10. Jim Lambek: "PERS and Exact Completions" ============================================================================= From rrosebru@mta.ca Fri May 16 16:22:04 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 May 2003 16:22:04 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Gkm1-0003Pn-00 for categories-list@mta.ca; Fri, 16 May 2003 16:21:45 -0300 Date: Fri, 16 May 2003 15:24:24 +1000 (EST) From: James Harland Subject: categories: Job Message-Id: <200305160524.h4G5OOr13718@goanna.cs.rmit.edu.au> Content-Type: text Sender: cat-dist@mta.ca Precedence: bulk Bcc: Status: O X-Status: X-Keywords: X-UID: 21 RMIT University School of Computer Science Faculty of Applied Science Lecturer Salary $38,159 - $76,961 p.a. +17% Super The School of Computer Science and Information Technology is one of Australia’s largest, priding itself on the quality of its graduates and international recognition for leading edge teaching and research in the field of Computer Science. Dedicated to the highest standards of education, research and community outreach, research and teaching is focused on the areas of:- Data Engineering eCommerce and Distributed Systems Emerging Technologies Enterprise Computing Intelligent Systems Software Engineering and Programming We are seeking a person who specialises in the area of Data Engineering, Software Engineering or Distributed Systems. Experienced IT professionals who have good academic backgrounds with strong management experience will also be considered. You will join a quality work environment, with research and teaching support, and professional development opportunities. For application details please visit the website listed below or contact Ms Brenda Jackson on +61 3 9925 2169. Quote Ref. No. 50003703. Applications close 2nd June 2003. http://www.rmit.edu.au/ps/jobs From rrosebru@mta.ca Sun May 18 13:10:24 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 18 May 2003 13:10:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19HQdl-0002m0-00 for categories-list@mta.ca; Sun, 18 May 2003 13:04:01 -0300 Message-ID: <1123.131.211.232.234.1053162731.squirrel@www.math.uu.nl> Date: Sat, 17 May 2003 11:12:11 +0200 (CEST) Subject: categories: 79th PSSL: Call for participation From: To: X-Priority: 3 Importance: Normal X-Mailer: SquirrelMail (version 1.2.11) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Virus-Scanned: by AMaViS snapshot-20020300 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 22 Dear all, We would like to invite you for the 79th meeting of the Peripatetic Seminar on Sheaves and Logic, which will be held in the weekend of the 28th and 29th of June near Utrecht, the Netherlands. It is organized by the University of Utrecht with financial support of the MRI, the Mathematical Research Institute. As a special attraction, Clemens Berger will give a tutorial on theta-categories, a topic from higher-dimensional category theory. For the entire weekend, we will stay at the conference centre "Kaap Doorn", near Utrecht (www.kaapdoorn.nl), which can easily be reached by public transport. Concerning these and other matters a webpage can be consulted, one that is at the moment under construction. The address will be: http://www.math.uu.nl/people/vdberg/PSSL79 Here we will also announce the precise costs for the stay at the conference centre. People who wish to attend the PSSL should send an e-mail to the address below. Please indicate if you want to give a talk. With best regards, The organizers, Jaap van Oosten Federico di Marchi Pieter Hofstra Claire Kouwenhoven-Gentil Benno van den Berg -- Benno van den Berg - Mathematisch Instituut, UU vdberg@math.uu.nl - P.O.box 80.010, 3508 TA Utrecht, NL -- From rrosebru@mta.ca Sun May 18 13:10:24 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 18 May 2003 13:10:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19HQfb-0002z6-00 for categories-list@mta.ca; Sun, 18 May 2003 13:05:55 -0300 Date: Sat, 17 May 2003 21:22:17 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: A name Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 It is well known that epimorphisms in rings do not have to be surjective. Suppose C is a category and R is a ring object in C. I am looking for a name to call maps X --> Y in C with the property that Hom(Y,R) --> Hom(X,R) is epic in rings. It is a kind of weak R-injectivity. Does anyone have a name for this? Michael From rrosebru@mta.ca Sun May 18 13:12:40 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 18 May 2003 13:12:40 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19HQlu-0003E9-00 for categories-list@mta.ca; Sun, 18 May 2003 13:12:26 -0300 Date: Fri, 16 May 2003 16:41:53 -0300 (BRT) From: Flavio Leonardo Cavalcanti de Moura To: Subject: categories: connected categories and epimorphisms. Message-ID: <20030516162342.M13454-100000@mx1.mat.unb.br> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1 Content-Transfer-Encoding: QUOTED-PRINTABLE X-Virus-Scanned: by AMaViS perl-10 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 Hi, How can I show that, in a connected category, projections (of the product) are epimorphisms? Thank you, Flavio Leonardo. From rrosebru@mta.ca Mon May 19 14:52:01 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 19 May 2003 14:52:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Hohy-0006b2-00 for categories-list@mta.ca; Mon, 19 May 2003 14:45:58 -0300 Date: Sun, 18 May 2003 14:19:19 -0400 (EDT) From: Peter Freyd Message-Id: <200305181819.h4IIJIgU022776@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: connected categories and epimorphisms. Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 The quickest natural example I know of a connected category in which projections from products needn't be epi is the category of commutative rings. Well, actually, the opposite category. The coproduct of Z_2 and Z_3 is the terminal ring. The two co-projections fail to be monic (the coproduct of a pair of objects in this category is their tensor product). From rrosebru@mta.ca Mon May 19 14:52:01 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 19 May 2003 14:52:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19HohT-0006Yn-00 for categories-list@mta.ca; Mon, 19 May 2003 14:45:27 -0300 Date: Sun, 18 May 2003 11:45:37 -0600 (MDT) From: Robin Cockett Subject: categories: Re: connected categories and epimorphisms. In-reply-to: <20030516162342.M13454-100000@mx1.mat.unb.br> To: categories@mta.ca Message-id: <0HF3009TMFEZKY@l-daemon> MIME-version: 1.0 Content-type: TEXT/plain; charset=us-ascii Content-transfer-encoding: 7BIT Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 Of course it depends rather heavily on what you mean by connected: (1) if you mean that there is a way to get between any two objects via arrows -- and one is allowed to go backwards along arrows -- then this is not true. Any category with products is necessarily connected in this manner and the category of Sets provides a counter-example. Any projection p_0: A x 0 -> A where 0 is the empty set and A is non-empty is non-epic. (2) if you mean that given any objects A and B there is always an arrow f: A -> B (differs from (1) in that you are not allowed to go backwards along arrows) -- that is homsets are non-empty -- then this IS true. This is because every projection in such a category has a section as the composite <1_A,f> p_0 A --------> A x B --------> A is the identity. This makes the projection a retraction and thus epic. (2) if you mean (stretching a bit) that every object has a (regular) epic onto the final object (all objects have global support) then all you need in addition is that the product functors _ x A preserves these epics. This will be the case, for example, if the category is cartesian closed ... however, such a category better not have an initial object! -robin On 16 May, Flavio Leonardo Cavalcanti de Moura wrote: > Hi, > > How can I show that, in a connected category, projections (of the > product) are epimorphisms? > > Thank you, > > Flavio Leonardo. From rrosebru@mta.ca Tue May 20 16:09:05 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 May 2003 16:09:05 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ICOV-0005CB-00 for categories-list@mta.ca; Tue, 20 May 2003 16:03:27 -0300 Date: Mon, 19 May 2003 14:27:00 +0200 (MET DST) Message-Id: <200305191227.OAA06052@luxuria.lsi.upc.es> To: categories@mta.ca Subject: categories: ETAPS 2004: FIRST CALL FOR SUBMISSIONS Sender: cat-dist@mta.ca Precedence: bulk From: cat-dist@mta.ca Status: RO X-Status: X-Keywords: X-UID: 27 [note from moderator: if you do follow the instructions at the start of the following message, please don't cc to categories... ] Please apologize if you receive multiple copies of this message. ********************************************************** *** ETAPS 2004 *** *** March 27 - April 4, 2004 *** *** Barcelona, SPAIN *** *** *** *** http://www.lsi.upc.es/etaps04/ *** ********************************************************** The European Joint Conferences on Theory and Practice of Software (ETAPS) is the primary European forum for academic and industrial researchers worki= ng on topics related to Software Science. It is a confederation of five main conferences, a number of satellite workshops and other events. ------------------------------------------------------------------------ 5 Conferences - 22 Satellite Workshops - Tutorials - Tool Demonstrations ------------------------------------------------------------------------ ********************************************************** *** *** *** CALL FOR SUBMISSIONS *** *** Submission deadline: October 17, 2003 *** *** *** ********************************************************** ----------------------------------------------------------------------- Conferences ----------------------------------------------------------------------- CC 2004: International Conference on Compiler Construction http://www.research.ibm.com/CC2004/home.html Chair: Evelyn Duesterwald (IBM, USA) duester@us.ibm.com ESOP 2004, European Symposium On Programming http://www.cis.ksu.edu/santos/esop2004/ Chair: David Schmidt (Kansas, USA) schmidt@cis.ksu.edu FASE 2004, Fundamental Approaches to Software Engineering http://ctp.di.fct.unl.pt/~mw/conf/fase04/ Co-Chairs: Tiziana Margaria (Dortmund, Germany) tmargaria@metaframe.de Michel Wermelinger (Lisboa, Portugal) mw@di.fct.unl.pt FOSSACS 2004 Foundations of Software Science and Computation Structures http://www.labri.fr/Perso/~igw/FOSSACS/ Chair: Igor Walukiewicz (Bordeaux, France) igw@labri.fr TACAS 2003, Tools and Algorithms for the Construction and Analysis of Syste= ms http://www.daimi.au.dk/~cpn/tacas04/ Co-Chairs: Kurt Jensen (Aarhus, Denmark) kjensen@daimi.au.dk Andreas Podelski (Saarbr=FCcken, Germany) podelski@mpi-sb.mpg.d= e ----------------------------------------------------------------------- ETAPS main conferences accept two types of contributions: * Research papers; * Tool demonstration papers. ----------------------------------------------------------------------- Research papers: ----------------------------------------------------------------------- Prospective authors are invited to submit full papers in English presenting original research. Submitted papers must be unpublished and not submitted for publication elsewhere. In particular, simultaneous submission of the same contribution to multiple ETAPS conferences is forbidden. The proceedings will be published in the Springer-Verlag Lecture Notes in Computer Science series. Final papers will be no more than 15 pages long in the format specified by Springer-Verlag at http://www.springer.de/comp/lncs/authors.html. It is recommended that submissions adhere to that format and length. Submissions that are clearly too long may be rejected immediately. Instructions on how to submit are available at the URL of each individual conference. ----------------------------------------------------------------------- Tool demonstration papers: ----------------------------------------------------------------------- Demonstrations of novel and state-of-the-art tools are also invited. A submission should have a clear connection to one of the main ETAPS conferences, possibly complementing a paper submitted separately= =2E Tool demonstrations are an integrated part of the ETAPS programme. Selected demonstrations will be presented in ordinary conference sessions, using state-of-the-art projection. The time allowed will be approximately the same as that for the presentation of a research paper. The demonstratio= n will be accompanied by the publication of a short paper (up to 4 pages) in the proceedings of the relevant ETAPS conference, describing the main featu= res of the tool. There will be opportunities for follow-up demonstrations with individuals and small groups. Submissions should follow the instructions published in the URL of the relevant conference. They should take the form of a self-contained tool description of no more than 4 pages in the format specified by Springer-Verlag at http://www.springer.de/comp/lncs/authors.html. The tool description should be accompanied by an appendix (not intended for publication, and not included in the page limit) indicating which features of the tool would be demonstrated - preferably with some sample screen snapshots - followed by a detailed specification of the hardware, software, and licensing requirements for installing and using the tool. N.B. Tool demonstrations should not be confused with research contributions to the TACAS conference, which emphasizes principles of tool design, implementation, and use, rather than focusing on specific domains of application. ----------------------------------------------------------------------- Satellite Workshops ----------------------------------------------------------------------- * A-UML - Agents and UML Contact: Marc-Philippe Huget (M.P.Huget@csc.liv.ac.uk) URL: http://www.informatik.uni-augsburg.de/auml2004 * AVIS'04 - Third International Workshop on Automatic Verification of Infinite-State Systems Contact: Dr. Ramesh Bharadwaj (ramesh@itd.nrl.navy.mil) URL: http://chacs.nrl.navy.mil/AVIS04 * CMCS 2004 - Coalgebraic Methods in Computer Science 2004 Contact: Jiri Adamek (J.Adamek@tu-bs.de) URL: http://www.iti.cs.tu-bs.de/~cmcs/ * COCV - 3rd International Workshop on Compiler Optimization Meets Compiler Verification Contact: Jens Knoop (Jens.Knoop@FernUni-Hagen.De) URL: http://sunshine.cs.uni-dortmund.de/~knoop/COCV2004/cocv2004.html * CP+CV'04 - Workshop on Constraint Programming and Constraints for Verification Contact: Thom Fruehwirth (Thom.Fruehwirth@informatik.uni-ulm.de) URL: http://www.informatik.uni-ulm.de/pm/mitarbeiter/fruehwirth/cp_etaps= 04.html * DCC - Designing Correct Circuits Contact: Mary Sheeran (ms@cs.chalmers) and Tom Melham (Tom.Melham@comlab.ox.ac.uk) URL: http://www.cs.chalmers.se/~ms/DCC04/ * FESCA - Formal Foundation of Embedded Software and Component-based Software Architectures Contact: Juliana K=FCster Filipe (jkfilipe@inf.ed.ac.uk) URL: http://www.csse.monash.edu.au/fesca email: fesca-04@inf.ed.ac.uk * FUSE 2004 - Foundations of Unanticipated Software Evolution Contact: Tom Mens, (Tom.Mens@vub.ac.be) URL: http://joint.org/fuse2004/ * GT-VMT - Graph Transformation and Visual Modelling Techniques Contact: Reiko Heckel URL: http://www.uni-paderborn.de/cs/ag-engels/GT-VMT04 email: gtvmt04@upb.de * INT - Third International Workshop on Integration of Specification Techniques for Applications in Engineering Contact: Hartmut Ehrig (ehrig@cs.tu-berlin.de) and Gunnar Schroeter (schroetg@cs.tu-berlin.de) URL: http://tfs.cs.tu-berlin.de/~gschroet/int04/index.html * LDTA - Fourth Workshop on Language Descriptions, Tools and Applications Contact: Joao Saraiva (jas@di.uminho.pt) URL: http://www.di.uminho.pt/LDTA04 * MBT 2004 - International Workshop on Model-Based Testing Contact: Alexander Kossatchev (kos@ispras.ru) URL: http://www.ispras.ru/news/MBT2004.html * QAPL'04 - 2nd Workshop on Quantitative Aspects of Programming Languages Contact: Alessandra Di Pierro URL: http://qapl04.di.unipi.it/ email: qapl04@di.unipi.it * RV'04 - Fourth Workshop on Runtime Verification Contact: Klaus Havelund (havelund@email.arc.nasa.gov) URL: http://ase.arc.nasa.gov/rv2004 * SC 2004 - Software Composition Contact: Uwe Assmann (uweas@ida.liu.se) URL: http://www.ida.liu.se/~uweas/sc2004 * SFEDL - Semantic Foundations of Engineering Design Languages Contact: Michael Mendler (michael.mendler@wiai.uni-bamberg.de) URL: http://www.uni-bamberg.de/~ba7gi99/sfedl04/ * SLAP 2004 : Synchronous Languages, Applications, and Programs Contact: Florence Maraninchi (Florence.Maraninchi@imag.fr) URL: http://www.inrialpes.fr/pop-art/people/girault/Slap04 * SPIN - 11th International Workshop on Model-Checking of Software Contact: Susanne Graf, Verimag/CNRS (spin04@imag.fr) URL: http://www-verimag.imag.fr/SPIN-2004 * TACoS - Test and Analysis of Component-Based Systems Contact: Mauro Pezz=E8 (pezze@disco.unimib.it) URL: www.lta.disco.unimib.it/tacos * WADT'04 - 17th International Workshop on Algebraic Development Techniques Contact: Fernando Orejas (orejas@lsi.upc.es) * WITS'04 - Workshop on Issues in the Theory of Security Contact: Peter Y A Ryan (peter.ryan@ncl.ac.uk) URL: http://www.dsi.unive.it/IFIPWG1_7/wits2004.html * WRLA 2004 - 5th International Workshop on Rewriting Logic and its Applications Contact: Narciso Marti-Oliet (narciso@sip.ucm.es) URL: http://www.fdi.ucm.es/wrla2004 email: wrla2004@sip.ucm.es ----------------------------------------------------------------------- Tutorials ----------------------------------------------------------------------- Proposals for half-day or full-day tutorials related to ETAPS 2004 are invited. Tutorial proposals will be evaluated on the basis of their assessed benefit for prospective participants to ETAPS 2004. Proposals should include a description of the material that will be covered in the tutorial; a justification of the relevance of the tutorial for ETAPS 2004; a short history of the tutorial if it has been given before; the duration of the tutorial; scope of the tutorial; the key learning objectives for the participants; the intended audience for the tutorial and required background; and the credentials for the instructor(s). Contact: Jordi Cortadella - http://www.lsi.upc.es/~jordic/ ----------------------------------------------------------------------- INVITED SPEAKERS ----------------------------------------------------------------------- Serge Abiteboul, INRIA-Rocquencourt, France Hubert Comon, Cachan, France Robin Milner, Cambridge, UK Peter O'Hearn, London, UK Gruia-Catalin Roman, Washington Univ., USA Mary Lou Soffa, Pittsburgh, USA Antti Valmari, Tampere, Finland ----------------------------------------------------------------------- IMPORTANT DATES ----------------------------------------------------------------------- October 17, 2003 Submission deadline for the main conferences and tutori= als December 12, 2003 Notification of acceptance/rejection January 9, 2004 Camera-ready version due March 29 - April 2, 2004 ETAPS 2004 main conferences March 27 - April 4, 2004 ETAPS 2004 satellite events ----------------------------------------------------------------------- ----------- you received this e-mail via the individual or collective address categories@mta.ca to unsubscribe from ETAPS list: contact etaps04@lsi.upc.es ----------- From rrosebru@mta.ca Tue May 20 16:09:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 May 2003 16:09:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ICSL-0005mO-00 for categories-list@mta.ca; Tue, 20 May 2003 16:07:25 -0300 From: Steve Stevenson MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16074.18059.966602.668242@merlin.cs.clemson.edu> Date: Tue, 20 May 2003 11:15:23 -0400 (EDT) To: categories@mta.ca Subject: categories: Automata as Categories Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 28 I am interested to find an article or book that is a category- theoretic redevelopment of "classical" automata. I'd like to find something that graduate students could use if they had already had an automata course and now would retrace that same development using category-theoretic vocabulary and means. Thanks in advance... steve From rrosebru@mta.ca Tue May 20 16:09:11 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 May 2003 16:09:11 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ICSc-0005po-00 for categories-list@mta.ca; Tue, 20 May 2003 16:07:42 -0300 Date: Tue, 20 May 2003 11:34:00 -0400 (EDT) From: Peter Freyd Message-Id: <200305201534.h4KFY00t020091@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Yikes Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 29 Peter Johnstone has pointed out to me that there is, of course, a much easier example of a category in which projections from products needn't be epi: the good ol' category of sets. As they say, the empty set really does exist. From rrosebru@mta.ca Tue May 20 16:09:05 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 May 2003 16:09:05 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ICRh-0005f6-00 for categories-list@mta.ca; Tue, 20 May 2003 16:06:45 -0300 From: Nikita Danilov MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16073.61856.465785.65278@laputa.namesys.com> Date: Tue, 20 May 2003 13:13:04 +0400 X-PGP-Fingerprint: 43CE 9384 5A1D CD75 5087 A876 A1AA 84D0 CCAA AC92 X-PGP-Key-ID: CCAAAC92 X-PGP-Key-At: http://wwwkeys.pgp.net:11371/pks/lookup?op=get&search=0xCCAAAC92 To: categories@mta.ca Subject: categories: Re: connected categories and epimorphisms. In-Reply-To: <200305181819.h4IIJIgU022776@saul.cis.upenn.edu> References: <200305181819.h4IIJIgU022776@saul.cis.upenn.edu> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 Peter Freyd writes: > The quickest natural example I know of a connected category in which > projections from products needn't be epi is the category of > commutative rings. Well, actually, the opposite category. The > coproduct of Z_2 and Z_3 is the terminal ring. The two > co-projections fail to be monic (the coproduct of a pair of objects in > this category is their tensor product). > It is interesting that construction of the coproduct in the category of "just" rings (associative, unitary, but not necessary commutative) is not easy to find in the literature. It seems, however, that it is relatively easy to construct: for given rings R1 and R2, let M1 and M2 be their multiplicative monoids and M be coproduct of M1 and M2 in the category of monoids. Form monoid ring of M over Z. That is, form free abelian group generated by underlying set of M and extend multiplication from generators by distributivity. Let's call resulting ring G. Let K be ideal in G generated by all elements of the form (A + B) - A - B, where both A and B belong to the same ring: either R1 or R2. That is, in ((A + B) - A - B) "+" is addition in R1 or R2, and "-" is subtraction in G. Now, quotient G/K is a coproduct of R1 and R2 in the category of rings, which is easy to prove using universal properties of coproduct M, monoid ring G, and epicness of the projection G ->> G/K. Is there more "direct" description of coproduct in the category of rings? > > Nikita. From rrosebru@mta.ca Wed May 21 15:48:39 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 May 2003 15:48:39 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19IYaW-0005tR-00 for categories-list@mta.ca; Wed, 21 May 2003 15:45:20 -0300 Date: Tue, 20 May 2003 21:42:26 +0200 (MEST) From: Taylor Paul Message-Id: <200305201942.h4KJgQTV014237@pianeta.di.unito.it> To: categories@mta.ca Subject: categories: localy compact spaces - computably based and over a topos Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 Drafts of two new papers on Abstract Stone Duality are now available, and I would very much appreciate your comments about them. Computably based locally compact spaces An elementary theory of the category of locally compact locales http://www.di.unito.it/~pt/ASD These two papers bring ASD into line with the "official" theory of locally compact sober spaces and locales, in two completely different ways. The ASD "Manifesto" was also revised recently. =================================== Computably based locally compact spaces The first paper shows that the main version of ASD is equivalent to the category of "computably based" locally compact locales, and computably continuous functions. By a "basis" I mean a family of open subspaces U^n and accompanying family of compact subspaces K^n, the topological information being captured by the inclusion relation K^n subset U^m. For locales the corresponding idea is the "way below" relation. The finitary properties of this are characterised, including in particular the "Wilker condition" concerning the inclusion of a compact subspace in the union of two open ones. The motivation of the paper is principally how to "import" traditional topology into ASD, using the real line as a running example. This paper is the expanded version of the one that I presented at "Category Theory and Computer Science" in Ottawa and the "Domains Workshop" in Birmingham last August/September. =================================== An elementary theory of the category of locally compact locales The second paper shows that, when we add an "underlying set" axiom, the category becomes equivalent to the category of locally compact locales over any elementary topos. The usual structure of locale theory (direct and inverse image maps, Heyting implication, etc) is DERIVED, in a type-theoretic style. This is a new characterisation, not only of this category of spaces, but also of elementary toposes themselves. (The same technique can be applied to the opposite of the category of constructively completely distributive lattices, but I haven't filled in the details of this yet.) ASD axiomatises its category of spaces directly, not starting from a category of sets. However, the full subcategory of overt discrete spaces has emerged to fill this role. In the traditional situation, the forgetful functor from spaces to sets has both adjoints (the discrete and indiscriminate topologies), but of these three functors, only the leftmost exists in standard ASD. This paper postulates its right adjoint, which yields the couniversal overt discrete object related to any given space. (Such a thing would be unacceptable in the main theory, as the equality predicate on the underlying set of the powerset of N would solve the Halting Problem.) Whereas the category of sets is an (often unstated) assumption in a typical mathematical discourse, in this case the topos itself is constructed from the axioms, viz as this full subcategory. More significantly, the infinitary joins that are needed to axiomatise either traditional topology or locale theory are also a consequence of the axioms, and not a part of them. This is the sense in which the new axiomatisation deserves to be called elementary. In fact, the logical power of the theory (powersets in the topos, and the infinitary joins) arises out of the ``underlying set'' assumption. We have another example to show that closure of a full subcategory under (co)limits is a long way from providing an adjoint, and indeed the existence of the adjoint can be very strong foundational principle in itself. For example, when well-foundedness is presented in categorical terms using coalgebras, the extensional ones form a reflective subcategory, but the axiom of replacement may be needed to construct the reflection functor. See Exercise 9.62 in my book, "Practical Foundations of Mathematics". Paul Taylor pt@di.unito.it From rrosebru@mta.ca Wed May 21 15:48:39 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 May 2003 15:48:39 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19IYav-0005xG-00 for categories-list@mta.ca; Wed, 21 May 2003 15:45:45 -0300 Date: Tue, 20 May 2003 15:57:55 -0400 (EDT) From: John Maweu To: Steve Stevenson Subject: categories: re: Automata as Categories In-Reply-To: <16074.18059.966602.668242@merlin.cs.clemson.edu> Message-ID: References: <16074.18059.966602.668242@merlin.cs.clemson.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 46 Hi, On Tue, 20 May 2003, Steve Stevenson wrote: > > I am interested to find an article or book that is a category- > theoretic redevelopment of "classical" automata. I'd like to find > something that graduate students could use if they had already had an > automata course and now would retrace that same development using > category-theoretic vocabulary and means. > > Thanks in advance... > > steve > Are you looking for more than the examples in Arrows, Structures, and Functors by Arbib and Manes? -o- From rrosebru@mta.ca Wed May 21 15:49:17 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 May 2003 15:49:17 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19IYdQ-0006Hs-00 for categories-list@mta.ca; Wed, 21 May 2003 15:48:20 -0300 Mime-Version: 1.0 Message-Id: In-Reply-To: <16074.18059.966602.668242@merlin.cs.clemson.edu> References: <16074.18059.966602.668242@merlin.cs.clemson.edu> Date: Tue, 20 May 2003 22:45:42 +0100 To: Steve Stevenson , categories@mta.ca From: Micheal Mac an Airchinnigh Subject: categories: re: Automata as Categories Content-Type: text/plain; charset="iso-8859-1" ; format="flowed" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 47 At 11:15 -0400 2003/20/05, Steve Stevenson wrote: >I am interested to find an article or book that is a category- >theoretic redevelopment of "classical" automata. I'd like to find >something that graduate students could use if they had already had an >automata course and now would retrace that same development using >category-theoretic vocabulary and means. > >Thanks in advance... > >steve --- Hi Steve! In my opinion, you're looking for stuff on M-categories (M a Monoid) and you're searching under keywords like "action" --- initially left! There is good material in Barr & Wells 1999. (The 3rd edition) or better groundwork --- Lawvere and Rosebrugh 2003 [ though much of what you eventually need is in the exercises :) ] Micheal -- ... o O o O o ... USUK WAR ON UN 20030320+... USUK WAR PART II 20030501+... ... o O o O o ... --- M=EDche=E1l Mac an Airchinnigh 5 Parson's Street Maynooth, Co. Kildare, Ireland mailto:micheal1@mac.com mailto:mmaa@eircom.net From rrosebru@mta.ca Wed May 21 15:52:37 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 May 2003 15:52:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19IYg3-0006d4-00 for categories-list@mta.ca; Wed, 21 May 2003 15:51:03 -0300 From: Juergen Koslowski Message-Id: <200305210719.h4L7Jca01230@lxt5.iti.cs.tu-bs.de> Subject: categories: Re: Automata as Categories To: categories@mta.ca Date: Wed, 21 May 2003 09:19:30 +0200 (CEST) X-Mailer: ELM [version 2.5 PL6] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 48 Steve Stevenson asked > I am interested to find an article or book that is a category- > theoretic redevelopment of "classical" automata. I'd like to find > something that graduate students could use if they had already had an > automata course and now would retrace that same development using > category-theoretic vocabulary and means. Dear Steve, I'd be interested in such pointers as well, especially since "classical automata theory" is a rather horrible mess. You may want to check out - Edwin Stewart Bainbridge's thesis "A unified minimal realization theory with duality", PhD Thesis, U. of Michigan, 1972. - R. Betti, "Automi e categorie chiuse" Boll. Un. Mat. Ital. A (5)\(1980), 44--58 - Kasangian, Kelly, and Rossi "Cofibrations and the realization of non-deterministic automata", Cahiers Topologie Geom. Diff. 24, 1 (1983), 23--46. Also, Mark William Hopkins presents some interesting ideas on his WEB-page . A pointer to the coalgebraic view of automata is Jan Rutten's page . You may want to start with "Automata and coinduction (an exercise in coalgebra). Technical Report SEN-R9803", which is available for downloading. Cheers, -- Juergen -- Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj@iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR) From rrosebru@mta.ca Thu May 22 11:13:08 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 May 2003 11:13:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19IqjH-0004ZL-00 for categories-list@mta.ca; Thu, 22 May 2003 11:07:35 -0300 X-Originating-IP: [158.59.27.31] X-Originating-Email: [harbaugh_keith@hotmail.com] From: "Keith Harbaugh" To: categories@mta.ca Subject: categories: Re: Automata as Categories Date: Thu, 22 May 2003 01:36:09 +0000 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 22 May 2003 01:36:10.0390 (UTC) FILETIME=[85D5A360:01C32002] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 49 A textbook (unfortunately long out of print) that seems quite suitable in both content and level to your need is: Ehrig, Kiermeier, Kreowski and K\:uhnel Universal Theory of Automata Teubner, 1974, 240pp. Also, in response Juergen's remark that "classical automata theory" is a rather horrible mess, one most distinguished categorist evidently agreed with him and responded by writing two ~400 page books on the subject: Samuel Eilenberg Automata, Languages and Machines Academic Press, 1974 and 1976. They make no explicit use of categorical notions nor language, but considering the author and date the categorical spirit surely prevails. Note also his book with Elgot on Recursiveness. Best, Keith >From: Steve Stevenson >To: categories@mta.ca >Subject: categories: Automata as Categories >Date: Tue, 20 May 2003 11:15:23 -0400 (EDT) >I am interested to find an article or book that is a category- >theoretic redevelopment of "classical" automata. I'd like to find >something that graduate students could use if they had already had an >automata course and now would retrace that same development using >category-theoretic vocabulary and means. From rrosebru@mta.ca Tue May 27 17:17:24 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 May 2003 17:17:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19KkrT-0005N2-00 for categories-list@mta.ca; Tue, 27 May 2003 17:15:55 -0300 Message-ID: <3ED34194.9050005@informatik.uni-bremen.de> Date: Tue, 27 May 2003 12:44:36 +0200 From: Till Mossakowski User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.3) Gecko/20030313 X-Accept-Language: en-us, en MIME-Version: 1.0 To: Categories Subject: categories: Topos logic arises naturally Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 50 You see: even with just aesthetic and software engineering considerations you are eventually lead to topos logic... -- Till Mossakowski Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen till@tzi.de P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till Message-Id: <200305270616.h4R6G3w8008134@plxc2089.pdx.intel.com> To: Randy Pollack cc: John Harrison , isabelle-users@cl.cam.ac.uk Subject: Re: HOL without description operators Date: Mon, 26 May 2003 23:16:03 -0700 From: John R Harrison Sender: Larry Paulson Hi Randy, | Perhaps more usefully, how do you suggest I do this task of developing HOL | without description operators. You might find it interesting to look at HOL Light. This gives a different axiomatization of the HOL logic, developed precisely because I was dissatisfied with the one in the original HOL system, on which I believe the Isabelle/HOL logic is based. Although I do eventually introduce the description operator, quite a lot of the basic logic --- including the automation of inductive definitions --- is developed without it (and indeed without excluded middle or extensionality). You may find it a more congenial starting-point. As Konrad Slind later pointed out, what I settled on is remarkably close to the internal logic of a topos, as presented for example in Lambek and Scott's book. This was a surprise to me since at that time I knew next to nothing about toposes and was motivated by a mixture of aesthetic and software engineering considerations. Cheers, John. From rrosebru@mta.ca Tue May 27 17:17:24 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 May 2003 17:17:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Kkpf-0005Eb-00 for categories-list@mta.ca; Tue, 27 May 2003 17:14:03 -0300 X-Originating-IP: [194.66.147.4] X-Originating-Email: [cft71@hotmail.com] From: "Christopher Townsend" To: categories@mta.ca Subject: categories: Can we construct free semi-lattice from free dist. lattice? Date: Tue, 27 May 2003 08:52:13 +0000 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 27 May 2003 08:52:13.0326 (UTC) FILETIME=[44399AE0:01C3242D] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 51 Dear All, I have a problem which I had thought very specialised, but actually can be stated very generally: - I have a category C with finite limits, and so I also have a category DLat(C) of distributive lattices which, lets say, has coequalizers. If free distibrutive lattices can be constructed (i.e. if there exists F:C->DLat(C) left adjoint to the forgetful functor) then do free semilattices exist? Thanks, Christopher Townsend (OU) From rrosebru@mta.ca Tue May 27 20:05:46 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 May 2003 20:05:46 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19KnUY-0000fi-00 for categories-list@mta.ca; Tue, 27 May 2003 20:04:26 -0300 Date: Tue, 27 May 2003 21:52:21 +0100 (BST) From: "Prof. Peter Johnstone" To: categories@mta.ca Subject: categories: Re: Can we construct free semi-lattice from free dist. lattice? In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *19KlQj-0003n7-Ib*t1T2DscuJf6* Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 52 On Tue, 27 May 2003, Christopher Townsend wrote: > Dear All, > I have a problem which I had thought very specialised, but actually can be > stated very generally: - > > I have a category C with finite limits, and so I also have a category > DLat(C) of distributive lattices which, lets say, has coequalizers. If free > distibrutive lattices can be constructed (i.e. if there exists F:C->DLat(C) > left adjoint to the forgetful functor) then do free semilattices exist? > I suspect the answer is no, for irritatingly trivial reasons. If C is a pointed category (i.e. has a zero object), then any internal distributive lattice in C has its top and bottom elements equal, and so is degenerate (i.e. isomorphic to the terminal object 1). Hence the free-distributive-lattice functor exists, and is the constant functor with value 1. But I'm sure there must be examples of pointed, finitely complete categories which don't have a free-semilattice functor (though I have to admit I don't have one at my fingertips). Peter Johnstone From rrosebru@mta.ca Wed May 28 14:12:38 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 May 2003 14:12:38 -0300 Message-ID: <20030528160009.91912.qmail@web41412.mail.yahoo.com> From: cat-dist@mta.ca Date: Wed, 28 May 2003 14:06:02 -0300 From: Maurice Kianpi Subject: categories: Injective Objects in a Category of coalgebras To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=3Diso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 53 Dear All, Do injective objects exist in the category of the coalgebras of the functor Po(Ax-) where P is the power set functor and A a non empty set? If the answer is yes, can they be characterized? Best regards. Maurice =3D=3D=3D=3D=3D A bientot. Maurice ___________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en fran=E7ais ! Yahoo! Mail : http://fr.mail.yahoo.com From rrosebru@mta.ca Wed May 28 15:16:50 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 May 2003 15:16:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19L5S9-0003lR-00 for categories-list@mta.ca; Wed, 28 May 2003 15:15:09 -0300 Date: Wed, 28 May 2003 16:32:59 +0200 (CEST) From: Benno van den Berg Reply-To: Benno van den Berg Subject: categories: PSSL 79 - FINAL ANNOUNCEMENT To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: W7BPfPvHegumMj/t0uUSiA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.2 SunOS 5.8 sun4u sparc Message-Id: <20030528143259.981B2520CE@mail.math.uu.nl> X-Virus-Scanned: by AMaViS snapshot-20020300 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 54 PSSL 79 - DOORN, THE NETHERLANDS - FINAL ANNOUNCEMENT Dear all, This is the final announcement for the 79th meeting of the Peripatetic Seminar on Sheaves and Logic, which will be held in the weekend of the 28th and 29th of June in Doorn, a place near Utrecht, the Netherlands. It is organized by the University of Utrecht with financial support from the MRI, the Mathematical Research Institute. We are glad to announce that this edition will feature a 3 hours tutorial by Clemens Berger on the subject of theta-categories, a topic from higher-dimensional category theory. The other confirmed speakers so far, are: Steve Awodey (Carnegie Mellon) Erik Palmgren (Uppsala University) Jonas Eliasson (Uppsala University) Christopher Mulvey (University of Sussex) The PSSL will take place at the conference centre "Kaap Doorn". The conference centre also offers rooms and meals, but only people who react before Friday the 6th of June are guaranteed to be offered this opportunity. FOR THIS REASON WE KINDLY URGE THOSE WHO ARE INTERESTED TO REGISTER BEFORE THE 6TH OF JUNE. (People who respond at a later date may have to stay at a hotel. In that case, special arrangements have to be made.) The all-in price for staying at the conference centre is 200-250 euro's. For further information and the latest list of participants, please consult the webpage (now fully operational): http://www.math.uu.nl/people/vdberg/PSSL79 People who wish to attend the PSSL should send an e-mail to vdberg@math.uu.nl indicating whether they you want to give a talk. Questions should be posted to the same address. With best regards, The organizers, Jaap van Oosten Federico de Marchi Pieter Hofstra Claire Kouwenhoven-Gentil Benno van den Berg -- Benno van den Berg - Mathematisch Instituut, UU vdberg@math.uu.nl - P.O.box 80.010, 3508 TA Utrecht, NL From rrosebru@mta.ca Fri May 30 23:18:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 May 2003 23:18:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19LvtQ-0002MZ-00 for categories-list@mta.ca; Fri, 30 May 2003 23:14:48 -0300 Message-ID: <3ED786C3.3060007@bluewin.ch> Date: Fri, 30 May 2003 18:28:51 +0200 From: Krzysztof Worytkiewicz User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.1) Gecko/20020823 Netscape/7.0 X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: universal colimits in 2-cat Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 55 Dear All, Is anybody aware of a reference to the fact that small colimits are universal in 2-Cat ? Cheers Krzysztof From rrosebru@mta.ca Fri May 30 23:18:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 May 2003 23:18:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Lvu9-0002Np-00 for categories-list@mta.ca; Fri, 30 May 2003 23:15:33 -0300 Message-ID: <20030530201401.40220.qmail@web12203.mail.yahoo.com> Date: Fri, 30 May 2003 13:14:01 -0700 (PDT) From: Galchin Vasili Subject: categories: Semantic tableaux and intuitionistic logic To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 56 Hello, I am only familiar with semantic tableaux for classical propositional logic (and classical 1st order logic). It seems that as an inference system it is based squarely around the law of the excluded middle because it is essentially reductio ad absurdum. Hence, as an inference system it can't be simply modified for intuitionistic propositional calculus?? (Of course, I am bringing this because the role that Heyting algebras play in Topos theory). Regards, Bill Halchin From rrosebru@mta.ca Fri May 30 23:18:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 May 2003 23:18:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Lvsv-0002Kc-00 for categories-list@mta.ca; Fri, 30 May 2003 23:14:17 -0300 Message-ID: <3ED76C99.1020801@informatik.uni-bremen.de> Date: Fri, 30 May 2003 16:37:13 +0200 From: Till Mossakowski User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.3) Gecko/20030313 X-Accept-Language: en-us, en MIME-Version: 1.0 To: Categories Subject: categories: Re: Topos logic arises naturally References: <3ED34194.9050005@informatik.uni-bremen.de> <002801c326a1$05dc0000$f112fea9@essex.ac.uk> In-Reply-To: <002801c326a1$05dc0000$f112fea9@essex.ac.uk> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 57 I did not want to deny the need of mathematical thought, but I found this example of topos theory emerging unexpectedly quite pleasing. Note that the mail is *not* about Isabelle. Admittedly, I do not know anything about the quoted system HOL light, so I have not verified Slind's claim. Till Elwood Wilkins wrote: > Isabelle's internal logic is not constructive. The existential clause of the > BHK-interpretation is violated so that a consquence of "all unicorns have > horns" is that "some unicorn has a horn". The moral (biased towards > theorists): software engineering considerations are not enough, a coherant > philosophy of mathematics is also needed. > > Elwood > > ----- Original Message ----- > From: Till Mossakowski > To: Categories > Sent: Tuesday, May 27, 2003 11:44 AM > Subject: categories: Topos logic arises naturally > > > >>You see: even with just aesthetic and software engineering >>considerations you are eventually lead to topos logic... >> >>-- >>Till Mossakowski Phone +49-421-218-4683 >>Dept. of Computer Science Fax +49-421-218-3054 >>University of Bremen till@tzi.de >>P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till >> >>Message-Id: <200305270616.h4R6G3w8008134@plxc2089.pdx.intel.com> >>To: Randy Pollack >>cc: John Harrison , isabelle-users@cl.cam.ac.uk >>Subject: Re: HOL without description operators >>Date: Mon, 26 May 2003 23:16:03 -0700 >>From: John R Harrison >>Sender: Larry Paulson >> >>Hi Randy, >> >>| Perhaps more usefully, how do you suggest I do this task of developing > > HOL > >>| without description operators. >> >>You might find it interesting to look at HOL Light. This gives a >>different axiomatization of the HOL logic, developed precisely because I >>was dissatisfied with the one in the original HOL system, on which I >>believe the Isabelle/HOL logic is based. >> >>Although I do eventually introduce the description operator, quite a lot >>of the basic logic --- including the automation of inductive definitions >>--- is developed without it (and indeed without excluded middle or >>extensionality). You may find it a more congenial starting-point. >> >>As Konrad Slind later pointed out, what I settled on is remarkably close >>to the internal logic of a topos, as presented for example in Lambek and >>Scott's book. This was a surprise to me since at that time I knew next to >>nothing about toposes and was motivated by a mixture of aesthetic and >>software engineering considerations. >> >>Cheers, >> >>John. >> >> >> >> -- Till Mossakowski Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen till@tzi.de P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till From rrosebru@mta.ca Fri May 30 23:18:07 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 May 2003 23:18:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Lvrf-0002EB-00 for categories-list@mta.ca; Fri, 30 May 2003 23:12:59 -0300 Message-ID: <002801c326a1$05dc0000$f112fea9@essex.ac.uk> Reply-To: "Elwood Wilkins" From: "Elwood Wilkins" To: "Categories" References: <3ED34194.9050005@informatik.uni-bremen.de> Subject: categories: Re: Topos logic arises naturally Date: Fri, 30 May 2003 12:35:06 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 58 Isabelle's internal logic is not constructive. The existential clause of the BHK-interpretation is violated so that a consquence of "all unicorns have horns" is that "some unicorn has a horn". The moral (biased towards theorists): software engineering considerations are not enough, a coherant philosophy of mathematics is also needed. Elwood ----- Original Message ----- From: Till Mossakowski To: Categories Sent: Tuesday, May 27, 2003 11:44 AM Subject: categories: Topos logic arises naturally > You see: even with just aesthetic and software engineering > considerations you are eventually lead to topos logic... > > -- > Till Mossakowski Phone +49-421-218-4683 > Dept. of Computer Science Fax +49-421-218-3054 > University of Bremen till@tzi.de > P.O.Box 330440, D-28334 Bremen http://www.tzi.de/~till > > Message-Id: <200305270616.h4R6G3w8008134@plxc2089.pdx.intel.com> > To: Randy Pollack > cc: John Harrison , isabelle-users@cl.cam.ac.uk > Subject: Re: HOL without description operators > Date: Mon, 26 May 2003 23:16:03 -0700 > From: John R Harrison > Sender: Larry Paulson > > Hi Randy, > > | Perhaps more usefully, how do you suggest I do this task of developing HOL > | without description operators. > > You might find it interesting to look at HOL Light. This gives a > different axiomatization of the HOL logic, developed precisely because I > was dissatisfied with the one in the original HOL system, on which I > believe the Isabelle/HOL logic is based. > > Although I do eventually introduce the description operator, quite a lot > of the basic logic --- including the automation of inductive definitions > --- is developed without it (and indeed without excluded middle or > extensionality). You may find it a more congenial starting-point. > > As Konrad Slind later pointed out, what I settled on is remarkably close > to the internal logic of a topos, as presented for example in Lambek and > Scott's book. This was a surprise to me since at that time I knew next to > nothing about toposes and was motivated by a mixture of aesthetic and > software engineering considerations. > > Cheers, > > John. > > > > From rrosebru@mta.ca Mon Jun 2 10:17:48 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 02 Jun 2003 10:17:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Mp7M-0004FY-00 for categories-list@mta.ca; Mon, 02 Jun 2003 10:12:52 -0300 From: Jpdonaly@aol.com Message-ID: <1c5.9c17e04.2c097945@aol.com> Date: Fri, 30 May 2003 23:19:33 EDT Subject: categories: Function composition of natural transformations? (Pat Donaly) To: categories@mta.ca MIME-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 59 Here is a technical/pedagogical question which has been bothering me for about twelve years. In problem 5 on page 19 of "Categories for the Working Mathematician" (CWM), Saunders Mac Lane points out that a natural transformation may be fully extended to an intertwining function from one category to another, intertwining meaning (except in the void case), that the function transforms on one side according to its domain functor and on the other according to its codomain functor. Then on page 42 Mac Lane introduces what he calls "horizontal" composition diagramatically and without reference to the fully extended intertwining functions. But the function composite of such a pair of functions trivially intertwines the function composite of the domain functors with that of the codomain functors, and this function composition operation is very quickly verified to be "horizontal" composition when written in terms of restrictions to sets of objects. Thus Mac Lane and everyone else I have read leaves the impression that an honest verification of, say, the associativity of "horizontal" composition would require a somewhat involved diagrammatic demonstration which, in fact, would be nothing other than the hard way to prove the associativity of function composition. Presumably this has been noticed for a long, long time, but the 1998 edition of CWM did not mention it, and I can't help but be struck by the fact that other authors' terminologies leave the impression that they don't know or don't care that "horizontal", star or Godement composition is function composition. Notationally, I am bemused to see the standard symbol for function composition (the small circle) degraded into a generic symbol for the composition of just about any category, while a star or an asterisk is frequently used to denote what amounts to function composition done awkwardly. This worries me that I am somehow overlooking something fairly blatant. Can someone tell me what it is? Jpdonaly@aol.com