From MAILER-DAEMON Wed Aug 19 13:44:12 2009 Date: 19 Aug 2009 13:44:12 -0300 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1250700252@mta.ca> X-IMAP: 1246807380 0000000040 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 Sun Jul 5 12:18:43 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 05 Jul 2009 12:18:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MNTUD-0006eY-Kv for categories-list@mta.ca; Sun, 05 Jul 2009 12:18:37 -0300 Date: Wed, 01 Jul 2009 08:03:31 +0100 From: Alexander Kurz MIME-Version: 1.0 To: categories Subject: categories: Postdoc and PhD position in Coalgebraic Logic Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Alexander Kurz Message-Id: Status: O X-Status: X-Keywords: X-UID: 1 The EPSRC grant `Coalgbraic Logic: Expanding the Scope' is a joint project between Alexander Kurz (Leicester) and Achim Jung (Birmingham), seeking to employ a Postdoc in Leicester and a PhD student in Birmingham. The deadline to apply for the Postdoc position is 22 July 2009. For more information see http://www.cs.le.ac.uk/people/akurz/clexp.html The advert for the Postdoc position follows. === Applications are invited for a Research Associate to work with Dr. Alexander Kurz (Leicester) and Prof. Achim Jung (Birmingham) on the EPSRC-funded project `Coalgebraic Logic: Expanding the Scope'. Coalgebraic Logic aims at a uniform theory of transition systems (coalgebras) and their (typically modal) logics. Central notions are bisimilarity, co-induction, and initial and final semantics. Coalgebraic Logic is a young and quickly developing field closely related to areas such as domain theory, modal logic, Stone duality in mathematics and to program semantics, concurrency, process algebra in computer science. The aim of the project is to expand the state of the art in Coalgebraic Logic in 3 directions: (1) From modal logic to first-order logic; (2) to study axiomatically defined classes of coalgebras; (3) explore the relationship with domain theory and extend the expressiveness of logics obtained via Domain Theory in Logical Form. Applicants should have or be nearing completion of a PhD in an area relevant to Coalgebraic Logic. This includes, for example, modal and algebraic logic, domain theory, category theory, but also other aspects of theoretical computer science, in particular those related to program semantics and type theory. Applicants should have a proven track record demonstrating ability to write, present and publish research results in conferences and journals. The closing date for this post is midnight on 22 July 2009. Enquiries please email to Alexander Kurz. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sun Jul 5 12:19:24 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 05 Jul 2009 12:19:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MNTUt-0006hV-3d for categories-list@mta.ca; Sun, 05 Jul 2009 12:19:19 -0300 Date: Wed, 01 Jul 2009 11:43:47 -0400 From: jim stasheff MIME-Version: 1.0 To: algtop , Categories list Subject: categories: realized by fibrations Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: jim stasheff Message-Id: Status: O X-Status: X-Keywords: X-UID: 2 Suppose I have a sequence of (topological) operads or monads O \to P \to Q such that `all' corresponding representations in Top X \to Y \to Z are fibrations is this enough to tell us O \to P \to Q is a fibration? jim [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sun Jul 5 12:21:45 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 05 Jul 2009 12:21:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MNTX4-0006sl-3O for categories-list@mta.ca; Sun, 05 Jul 2009 12:21:34 -0300 MIME-version: 1.0 Content-type: text/plain; charset=ISO-8859-1; format=flowed Date: Fri, 03 Jul 2009 10:37:56 +0200 From: Fernando Muro To: categories@mta.ca Subject: categories: advanced course on TQFT Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Fernando Muro Message-Id: Status: O X-Status: X-Keywords: X-UID: 3 Dear colleagues, An Advanced Course on Topological Quantum Field Theories will take place=20 at the University of Almer=EDa from October 19th to 23rd, 2009. http://nevada.ual.es:81/topologia/curso.php This course aims to engage PhD students and postdoctoral researchers in=20 these new developments together with international experts in the field.=20 Lectures will be given by: * Joachim Kock (Universitat Aut=F2noma de Barcelona) * Andrey Lazarev (University of Leicester) * Gregor Masbaum (Institut de Math. de Jussieu / Universit=E9 Paris=20 Diderot, Paris 7) * Christoph Schweigert (Universit=E4t Hamburg) There will be a limited number of grants covering travel and lodging=20 expenses for young participants. The course will be followed by the XVI Spanish Topology Meeting from=20 October 23rd to 24th, 2009. http://nevada.ual.es:81/topologia/index.php The organizing committee is looking forward to meeting you soon in Almer=ED= a. David Llena (U. Almer=EDa) Fernando Muro (U. Barcelona) Frank Neumann (U. Leicester) Jos=E9 L. Rodr=EDguez Blancas (U. Almer=EDa, coordinador) Miguel =C1ngel S=E1nchez Granero (U. Almer=EDa) Antonio Viruel (U. M=E1laga) --=20 Fernando Muro Universitat de Barcelona, Departament d'=C0lgebra i Geometria http://atlas.mat.ub.es/personals/muro/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sun Jul 5 12:22:30 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 05 Jul 2009 12:22:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MNTXs-0006vV-6Z for categories-list@mta.ca; Sun, 05 Jul 2009 12:22:24 -0300 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Neil Ghani Subject: categories: PhD place Available Date: Fri, 3 Jul 2009 12:02:16 +0100 To: categories@mta.ca Sender: categories@mta.ca Precedence: bulk Reply-To: Neil Ghani Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 Dear All, Do any of you know a student who wants to do a PhD? We have a place available for anyone interested in type theory, category theory of functional programming. The student must a first class degree or masters with distinction All the best Neil [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 9 21:53:13 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Jul 2009 21:53:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4Ks-0003L0-P4 for categories-list@mta.ca; Thu, 09 Jul 2009 21:51:34 -0300 MIME-Version: 1.0 Date: Sun, 5 Jul 2009 19:31:43 -0500 Subject: categories: Re: Yoneda Theorem < Yoneda Lemma < Dense Yoneda Theorem From: Michael Shulman To: Vaughan Pratt , Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Shulman Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 On Sun, Jun 28, 2009 at 11:11 PM, Vaughan Pratt wrot= e: > (Incidentally, of what use are non-free cocompletions? =A0Is there any > reason not to define "cocompletion" to make it free? =A0I seem to recall > people being happy to drop "free" in this context. =A0Who ordered "free"?= ) To me the unadorned word "completion" connotes an idempotent operation, which the free (co)completion of a category is not. A more precise term would be "free cocomplete category generated by." Unlike most other uses of "complete" in mathematics, completeness of a category is not a property but a "property-like structure." Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 9 21:53:13 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Jul 2009 21:53:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4Jz-0003I3-Tj for categories-list@mta.ca; Thu, 09 Jul 2009 21:50:39 -0300 Date: Sun, 5 Jul 2009 21:54:50 +0100 (BST) From: "Prof. Peter Johnstone" To: Thomas Streicher , categories@mta.ca Subject: categories: Re: separable locale MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: "Prof. Peter Johnstone" Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 Dear Thomas, I'm pretty sure that what Michael meant by "separable" was what most topologists would call "second countable" -- i.e., countably generated as a frame. (There are some topology textbooks in which this condition is called "completely separable".) Peter Johnstone --------------------------------- On Tue, 30 Jun 2009, Thomas Streicher wrote: > Recently rereading Fourman's "Continuous Truth" I came across the term > "separable locale" but could nowhere find an explanation. Does it mean a > cHa A for which there exists a countable subset B such that ever a in A is > the supremum of those b in B with b leq a. This would be the point free > account of "second countable", i.e. having a countable basis. > Of course, second countable T_) spaces are separable, i.e. have a > countable > dense set. > Is this reading the "usual" one? > > Thomas > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 9 21:53:13 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Jul 2009 21:53:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4Lj-0003NG-HA for categories-list@mta.ca; Thu, 09 Jul 2009 21:52:27 -0300 Date: Mon, 06 Jul 2009 10:08:59 +0200 From: Andree Ehresmann To: Categories Subject: categories: Non-free cocompletions MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Andree Ehresmann Message-Id: Status: O X-Status: X-Keywords: X-UID: 7 Vaughan Pratt writes > Incidentally, of what use are non-free cocompletions? Is there any reason not to define "cocompletion" to make it free? I can indicate two important uses of non-free cocompletions, and more precisely cocompletions for particular classes of diagrams preserving some given colimits: 1. The construction of what, with Charles, we called the "prototype" and the "type" associated to a sketch (in "Categories of sketchd structures", Cahiers Top. et Geom. Diff. III-2, 1972) 2. The "complexification process" which, with Jean-Paul Vanbremeersch, we use extensively in our model for hierarchical evolutionary systems ("Memory Evolutive Systems: Hierarchy, Emergence, Cognition", Elsevier 2007) Kindly Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 9 21:53:52 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Jul 2009 21:53:52 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4N0-0003SH-B4 for categories-list@mta.ca; Thu, 09 Jul 2009 21:53:46 -0300 Date: Wed, 8 Jul 2009 19:06:27 +0200 From: gcuri@math.unipd.it To: Thomas Streicher , categories@mta.ca Subject: categories: Re: separable locale MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: gcuri@math.unipd.it Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 Dear Thomas, as far as I remember, Fourman & Grayson define and study separable locale= s toward the end of "Formal spaces". With best regards Giovanni Curi Quoting Thomas Streicher : > Recently rereading Fourman's "Continuous Truth" I came across the term > "separable locale" but could nowhere find an explanation. Does it mean = a > cHa A for which there exists a countable subset B such that ever a in A= is > the supremum of those b in B with b leq a. This would be the point free > account of "second countable", i.e. having a countable basis. > Of course, second countable T_) spaces are separable, i.e. have a > countable > dense set. > Is this reading the "usual" one? > > Thomas > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 10 08:26:25 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 10 Jul 2009 08:26:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPEDM-0001Ds-DG for categories-list@mta.ca; Fri, 10 Jul 2009 08:24:28 -0300 From: Thorsten Altenkirch To: categories List Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit Mime-Version: 1.0 (Apple Message framework v935.3) Subject: categories: coherence for lax monoidal cats Date: Thu, 9 Jul 2009 23:39:26 +0100 Sender: categories@mta.ca Precedence: bulk Reply-To: Thorsten Altenkirch Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 Hi, is there a coherence theorem for lax monoidal cats? I have alpha : (A (x) B) (x) C -> A (x) (B (x) C) rho : A -> A (x) I lambda : I (x) A -> A Do I need just the diagrams from MacLanes coherence theorem (suitably modified)? Or do I need additional ones? Cheers, Thorsten [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 10 08:26:25 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 10 Jul 2009 08:26:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPEER-0001IG-8J for categories-list@mta.ca; Fri, 10 Jul 2009 08:25:35 -0300 Date: Fri, 10 Jul 2009 00:32:02 -0300 From: "Eduardo J. Dubuc" To: "Prof. Peter Johnstone" , categories@mta.ca Subject: categories: Re: separable locale Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Eduardo J. Dubuc" Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 "separable" is used also to mean T_2 Prof. Peter Johnstone wrote: > Dear Thomas, > > I'm pretty sure that what Michael meant by "separable" was what > most topologists would call "second countable" -- i.e., countably > generated as a frame. (There are some topology textbooks in which > this condition is called "completely separable".) > > Peter Johnstone > --------------------------------- > On Tue, 30 Jun 2009, Thomas Streicher wrote: > >> Recently rereading Fourman's "Continuous Truth" I came across the term >> "separable locale" but could nowhere find an explanation. Does it mean a >> cHa A for which there exists a countable subset B such that ever a in >> A is >> the supremum of those b in B with b leq a. This would be the point free >> account of "second countable", i.e. having a countable basis. >> Of course, second countable T_) spaces are separable, i.e. have a >> countable >> dense set. >> Is this reading the "usual" one? >> >> Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 10 11:07:14 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 10 Jul 2009 11:07:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPGjl-0005Pi-VZ for categories-list@mta.ca; Fri, 10 Jul 2009 11:06:06 -0300 Date: Thu, 09 Jul 2009 17:33:29 +0300 From: Andrius Kulikauskas MIME-Version: 1.0 To: categories@mta.ca Subject: categories: An abstracted matrix approach to category theory? Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Andrius Kulikauskas Message-Id: Status: O X-Status: X-Keywords: X-UID: 11 I'm studying the basics of Category Theory. I appreciate help with my questions! My main interest is to "know everything and apply that knowledge usefully". I have a set of notes that reflect more than 25 years of work on this: http://www.worknets.org/wiki.cgi?LivingByTruth/Summary Category theory may be relevant in describing an "algebra of views" and the composition of views. Consider a lost child who goes to where she thinks her mother will look for her. Such a child is taking up her view of her mother's view of her view of her mother's view of her view. In this way, it is possible for two people to have a "good understanding" even if they presently have no channel of communication. http://www.worknets.org/wiki.cgi?LivingByTruth/LostChild Has anybody ever studied an algebra of views or perspectives? I'm studying from "Basic Category Theory for Computer Scientists" by Benjamin C. Pierce. I'm interested to apply the mathematics from my Ph.D. thesis "Symmetric Functions of the Eigenvalues of a Matrix" (UCSD, 1993). http://www.worknets.org/upload/AndriusKulikauskas/AndriusKulikauskasThesis.pdf I am wondering if it is possible to consider a category as an "abstracted matrix" and take its trace or determinant, etc. Symmetric functions are those functions such as X1 + X2 + X3 or X1*X2*X3 which stay the same even if you permute the variables. They are ubiquitous in algebraic combinatorics because objects are generally built up with labels (which may at some point taken off) where the order of the labels themselves generally shouldn't matter. I studied algebraic combinatorics as the "basement" of mathematics where objects are constructed, and thus in some sense, foundational. I was also interested that the vector space of symmetric functions had several "natural" bases, namely the power, elementary, homogeneous, monomial, forgotten, Schur which I thought might reflect how humans look at things. http://mathworld.wolfram.com/SymmetricFunction.html For my thesis, I noted that the trace and determinant of a matrix are symmetric functions of its eigenvalues, namely the sum E1 + E2 + E3 +... and the product E1*E2*E3... We can calculate these and all symmetric functions of eigenvalues straightforwardly in terms of the edges of a matrix, which is interesting, because in general, we can't calculate the eigenvalues themselves. I gave combinatorial interpretations of these functions in terms of walks, cycles, Lyndon words, rimhook tableux, etc on a generic matrix A. What's very interesting is that if you set that generic matrix A to be a diagonal matrix X (whose eigenvalues are necessarily the diagonal elements), then the results collapse to yield the usual symmetric functions. The matrix A can be specialized in other ways as well. Also, the symmetric functions of the eigenvalues capture the combinatorics of all of the theorems that I could find about generic matrices. I am drawn to think of a category as a "generic matrix" from the combinatorial point of view, if possible. In such a view: * the objects would be the dimensions of a square matrix A (and I allow that the objects are unordered and perhaps uncountable, so that I speak of an "abstracted matrix"). * each arrow F:X->Y would be a term in an (unordered, commutative) sum that corresponds to Axy * composition and associativity imply that each term in such a sum can be written (perhaps in more than one way) as a path (composed of arrows) starting at X and passing through perhaps several other nodes and arriving at Y. * an identity 1:X->X can be thought of as a term 1 in the series for the diagonal cell Axx (I suppose that the identity need not be unique? or must it?) * if there are no arrows from X to Y, then we write a 0 in the cell Axy What I would then want to say is that the series Axy consists of terms such that: * some are distinct atoms F:X->Y * the rest are generated by composition F:X-> ... ... ... ->Y * there is an equivalence relationship by which certain compositions are equal, perhaps imagined to collapse I suppose that this is alway possible in that, given X, Y, we can simply take as our "atoms" the entire collection of arrows from X to Y. Then all compositions must collapse back into our atoms. Indeed, there is a partial order (by inclusion) of the sets of arrows that may be understood as "the atoms". In this partial order we may ask if there is any set of arrows that is "natural", for example, depending on the equivalence relationship, there may or not be a smallest set of atoms. Perhaps this search for atoms might be analogous to what "representation theory" does for groups. This is a very "concrete" approach and when I wrote to Joseph Goguen (who sadly passed away) about it, he didn't think that was a good way to think about categories. But I have in my thesis a powerful perspective for dealing with a generic matrix. And I think that an "abstracted matrix" is metaphysically, conceptually about the most basic object that math offers. I suppose that my question is, Assuming a labeling for objects, What can we say about the systems for labeling arrows (the ones that drop parentheses, thanks to associativity)? Once we have a system for labeling the arrows, then my thesis work observes that various constructions accord with symmetric functions of "eigenvalues" of the related matrix. For example, the trace generates the closed walks (from any X back to itself) that you can take within the category. The determinant of a category is the product of signed cycles. The sign is straightforward if there is an implicit order in the objects, and if one does not exist for some of the objects, then we can simply leave that unresolved. Where the sign exists, then there can be some collapsing. Are there theorems in category theory where products of signed cycles are generated? Note that we may have two categories with the same objects (or we may always extend the sets of objects and embed the categories). Then multiplication of matrices gives a composition of the categories. We can multiply (and compose) a matrix with itself. (Indeed, a category may be thought of as the matrix generated from its atoms Q by series expansion matrix multiplication 1/(1-Q) ). And the matrix/category A may be thought as the paths accepted by an automata and Q as the basic rules. Has this "abstracted matrix" approach been taken? I appreciate suggestions on what to read and what to explore. Thank you, Andrius Kulikauskas Minciu Sodas http://www.ms.lt ms@ms.lt +370 699 30003 Dukiskiu km Butrimoniu sen Alytaus raj Lithuania [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sat Jul 11 11:04:47 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 11 Jul 2009 11:04:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPdAf-0001Vs-FG for categories-list@mta.ca; Sat, 11 Jul 2009 11:03:21 -0300 Date: Fri, 10 Jul 2009 18:32:07 +0200 Subject: categories: flat topologies From: "Szlachanyi Kornel" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-2 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Szlachanyi Kornel" Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 Dear List, I have some questions on flat functors and Grothendieck topologies. It is probably well-known that if F: C--> Set is a flat functor on a small category then there is a Grothendieck topology on C in which the covering sieves S on the object c consist of sets of arrows to c such that {Fs|s in S} is jointly epimorphic on Fc. 1. Could you tell me a reference for this statement? 2. Is there a characterization of Grothendieck topologies that arise in this way from a flat functor? (`flat topologies'?) 3. For what categories C will there be a flat functor inducing the canonical topology on C? Thank you for any help. Kornel --------------------------------------------------- Kornel Szlachanyi Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Science Budapest --------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sat Jul 11 11:04:48 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 11 Jul 2009 11:04:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPd9B-0001SQ-GT for categories-list@mta.ca; Sat, 11 Jul 2009 11:01:49 -0300 MIME-Version: 1.0 Subject: categories: RE: Non-free cocompletions Date: Fri, 10 Jul 2009 11:09:45 -0400 From: "Pieter Hofstra" To: Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Pieter Hofstra" Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 There are situations where standard completion constructions are = insufficient to accurately describe the relationship between two = categories. The motivating example in the paper "Relative completions" = (JPAA 192, 2004) was the presentation of the Effective topos as an exact = completion of the category of partitioned assemblies. This presentation = relies on the axiom of choice in Sets, and therefore does not work when = we work over an arbitrary base topos. The solution is to define a = relative version of the exact completion which preserves quotients of = equivalence relations coming from the base topos. More precisely, it is = defined by first freely adding all quotients, but then formally = inverting the canonical comparison morphisms between the new quotients = and the old ones from the base. Best regards, Pieter -----Original Message----- From: categories@mta.ca on behalf of Andree Ehresmann Sent: Mon 7/6/2009 4:08 AM To: Categories Subject: categories: Non-free cocompletions =20 Vaughan Pratt writes > Incidentally, of what use are non-free cocompletions? Is there any reason not to define "cocompletion" to make it free? I can indicate two important uses of non-free cocompletions, and more precisely cocompletions for particular classes of diagrams preserving some given colimits: 1. The construction of what, with Charles, we called the "prototype" and the "type" associated to a sketch (in "Categories of sketchd structures", Cahiers Top. et Geom. Diff. III-2, 1972) 2. The "complexification process" which, with Jean-Paul Vanbremeersch, we use extensively in our model for hierarchical evolutionary systems ("Memory Evolutive Systems: Hierarchy, Emergence, Cognition", Elsevier 2007) Kindly Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sat Jul 11 11:04:48 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 11 Jul 2009 11:04:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPdA7-0001UW-LU for categories-list@mta.ca; Sat, 11 Jul 2009 11:02:47 -0300 Subject: categories: Re: Yoneda Theorem < Yoneda Lemma < Dense Yoneda Theorem To: pratt@cs.stanford.edu, categories@mta.ca Date: Fri, 10 Jul 2009 13:07:28 -0300 (ADT) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: categories@mta.ca Precedence: bulk Reply-To: selinger@mathstat.dal.ca (Peter Selinger) Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 Vaughan Pratt wrote: > of what use are non-free cocompletions? Is there any > reason not to define "cocompletion" to make it free? Michael Shulman wrote: > To me the unadorned word "completion" connotes an idempotent operation The presheaf category [C^op,Set] is a co-completion of C. Its full subcategory of limit-preserving functors is another co-completion of C. Both are "free", but with respect to a different criterion: the Yoneda embedding into the first one does not preserve existing colimits, whereas into the second one it does. In particular, the second operation is idempotent (up to equivalence of categories) if C is already co-complete (this also follows from the adjoint functor theorem). It would therefore qualify as a "completion" in the sense that Mike Shulman mentioned. Any co-complete category between these two extremes is presumably also a (non-free) co-completion. -- Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sat Jul 11 11:05:57 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 11 Jul 2009 11:05:57 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPdCW-0001aH-02 for categories-list@mta.ca; Sat, 11 Jul 2009 11:05:16 -0300 From: peasthope@shaw.ca To: peasthope@shaw.ca Subject: categories: Category 2 Date: Fri, 10 Jul 2009 13:00:08 -0700 Sender: categories@mta.ca Precedence: bulk Reply-To: peasthope@shaw.ca Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 Folk, Several errors and omissions in the description of Category 2 have been corrected. http://carnot.yi.org/Category2.xhtml Firefox and Iceweasel can display it correctly. Other browsers have problems. On one MS-Win* system, the upper half brackets are absent. Most likely a font problem. Chrome mislocates lines or arrowheads or both and fails to apply some of the text in the SVG. I'm interested in any further criticisms and suggestions. Thanks, ... Peter E. -- Google "pathology workshop". [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sun Jul 12 09:31:30 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 12 Jul 2009 09:31:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPyBT-0002qT-UK for categories-list@mta.ca; Sun, 12 Jul 2009 09:29:35 -0300 Date: Sat, 11 Jul 2009 16:41:17 +0100 (BST) From: "Prof. Peter Johnstone" To: Szlachanyi Kornel , categories@mta.ca Subject: categories: Re: flat topologies MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: "Prof. Peter Johnstone" Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 Here's one way to look at it. A flat functor F: C --> Set corresponds to a point p of the presheaf topos [C^op,Set]. Given a Grothendieck topology J, p factors through the sheaf topos Sh(C,J) iff F carries J-covering sieves to epimorphic families. Thus the particular J you define is the largest for which p factors through Sh(C,J); equivalently, Sh(C,J) is the image (in the surjection--inclusion sense) of the geometric morphism p: Set --> [C^op,Set]. Hence a topos has a presentation of this kind iff it admits a surjective geometric morphism from Set; equivalently, iff it is (equivalent to) the category of coalgebras for a finite-limit-preserving accessible comonad on Set. Peter Johnstone ------------------- On Fri, 10 Jul 2009, Szlachanyi Kornel wrote: > Dear List, > > I have some questions on flat functors and Grothendieck topologies. > It is probably well-known that if F: C--> Set is a flat functor > on a small category then there is a Grothendieck topology on C > in which the covering sieves S on the object c consist of sets > of arrows to c such that {Fs|s in S} is jointly epimorphic on Fc. > > 1. Could you tell me a reference for this statement? > > 2. Is there a characterization of Grothendieck topologies that > arise in this way from a flat functor? (`flat topologies'?) > > 3. For what categories C will there be a flat functor inducing > the canonical topology on C? > > Thank you for any help. > > Kornel > > --------------------------------------------------- > Kornel Szlachanyi > Research Institute for Particle and Nuclear Physics > of the Hungarian Academy of Science > Budapest > --------------------------------------------------- > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Mon Jul 13 11:31:15 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 13 Jul 2009 11:31:15 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MQMVz-0000nH-Ot for categories-list@mta.ca; Mon, 13 Jul 2009 11:28:23 -0300 To: categories@mta.ca Subject: categories: FAST extension: 20 July (abstracts), 24 July (papers) From: "Joshua D. Guttman" Date: Sun, 12 Jul 2009 22:09:42 -0400 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: categories@mta.ca Precedence: bulk Reply-To: "Joshua D. Guttman" Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 The workshop on Formal Aspects of Security and Trust has Springer LNCS post-proceedings and a potential journal special issue. We're extending the deadline to 20 July for abstract submission and 24 July for the actual papers. Would you like to make a submission? It's been excellent the past several meetings. Regards -- Joshua ~~~~~~~~~~~~~~~~ *** Formal Aspects of Security and Trust *** *** Springer LNCS Post-proceedings *** *** *** *** Extended deadline: *** *** Abstract: 20 July 2009 *** *** Paper: 24 July 2009 *** *** *** *** Submission URL: *** *** http://www.easychair.org/conferences/?conf=fast2009 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 6th International Workshop on Formal Aspects of Security & Trust (FAST2009) 5-6 November 2009 Eindhoven, NL http://www.iit.cnr.it/FAST2009/ FAST2009 is an event of the Formal Methods Week http://www.win.tue.nl/fmweek/ FAST is under the auspices of IFIP WG 1.7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ OVERVIEW OF FAST The sixth International Workshop on Formal Aspects of Security and Trust (FAST2009) aims at continuing the successful efforts of the previous FAST workshops, fostering cooperation among researchers in the areas of security and trust. Computing and network infrastructures have become pervasive, and now they carry a great deal of economic activity. Thus, society needs well matching security and trust mechanisms. Interactions increasingly span several enterprises and involve loosely structured communities of individuals. Participants in these activities must control interactions with their partners based on trust policies and business logic. Trust-based decisions effectively determine the security goals for shared information and for access to sensitive or valuable resources. FAST focuses on the formal models of security and trust that are needed to state goals and policies for these interactions. We also seek new and innovative techniques for establishing consequences of these formal models. Implementation approaches for such techniques are also welcome. PAPER SUBMISSION Suggested submission topics include, but are not limited to: Formal models for security, trust and reputation Security protocol design and analysis Logics for security and trust Trust-based reasoning Distributed trust management systems Digital asset protection Data protection Privacy and ID management issues Information flow analysis Language-based security Security and trust aspects in ubiquitous computing Validation/Analysis tools Web/Grid services security/trust/privacy Security and risk assessment Resource and access control Case studies IMPORTANT DATES Title/Abstract Submission: 13 July Paper submission: 20 July Author Notification: 30 August Pre-proceedings version: 5 October Workshop: 5-6 November 2009 Post-proceedings version: 30 November 2009 Organizers . Pierpaolo Degano, University of Pisa, Italy . Joshua Guttman, Worcester Polytechnic Inst., USA Program Committee Gilles Barthe, IMDEA Software, Spain Fre'de'ric Cuppens, Telecom Bretagne, France Pierpaolo Degano, University of Pisa, Italy (co-chair) Theo Dimitrakos, BT, UK Sandro Etalle, Eindhoven, NL Roberto Gorrieri, Bologna, Italy Joshua Guttman, Worcester Polytechnic Inst., USA (co-chair) Masami Hagiya, Tokyo, Japan Chris Hankin, Imperial College (London), UK Bart Jacobs, Radboud University Nijmegen, NL Christian Jensen, DTU, Denmark Yuecel Karabulut, SAP Research, USA Igor Kotenko, SPIIRAS, Russia Fabio Martinelli, CNR, IT Catherine Meadows, Naval Research Lab, USA Ron van der Meyden, University of New South Wales, Australia Mogens Nielsen, Aarhus, Denmark Dusko Pavlovic, Kestrel Institute, USA and Oxford, UK Riccardo Pucella, Northeastern, USA Peter Ryan, Luxembourg Steve Schneider, Surrey, UK Jean-Marc Seigneur, University of Geneva, Switzerland PROCEEDINGS Post-proceedings of the workshop will be published with LNCS. A special journal issue is also planned. SUBMISSION GUIDELINES: *** http://www.easychair.org/conferences/?conf=fast2009 *** We seek papers presenting original contributions. Two types of submissions are possible: (1) short papers, up to 5 pages in LNCS format, (2) full papers, up to 15 pages in LNCS format. Submissions should clearly state their category (1 or 2). Author's full name, address, and e-mail must appear on the first page. Accepted full papers will be published in the formal post-proceedings in LNCS. Short papers as well as full papers will be included in the informal proceedings distributed at the workshop. After the workshop, authors of short papers which are judged mature enough for publication will be invited to submit full papers. These will be reviewed according to the usual refereeing procedures, and accepted papers will be published in the post-proceedings in LNCS. Simultaneous submission of full papers to a journal or conference/workshop with formal proceedings justifies rejection. Short papers at FAST are not formally published, so this restriction does not apply to them. However, related publications and overlapping submissions must be cited explicitly in short papers. -- Joshua D. Guttman The MITRE Corporation [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 14 09:58:14 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 14 Jul 2009 09:58:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MQhYe-0004wI-7Y for categories-list@mta.ca; Tue, 14 Jul 2009 09:56:32 -0300 MIME-version: 1.0 Date: Mon, 13 Jul 2009 17:44:53 -0400 From: Jules Desharnais To: Jules.Desharnais@ift.ulaval.ca Subject: categories: Call for papers: Mathematics of Program Construction Content-type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Jules Desharnais Message-Id: Status: O X-Status: X-Keywords: X-UID: 18 FIRST CALL FOR PAPERS 10th International Conference on Mathematics of Program Construction MPC 2010 Qu=E9bec City, Canada, 21-23 June 2010 http://mpc-amast2010.fsg.ulaval.ca/ Colocated with AMAST 2010 (23-26 June 2010) BACKGROUND The biennial MPC conferences aim to promote the development of mathematical principles and techniques that are demonstrably practical and effective in the process of constructing computer programs. Topics of interest range from algorithmics to support for program construction in programming languages and systems. The previous conferences were held in Twente, The Netherlands (1989), Oxford, UK (1992), Kloster Irsee, Germany (1995), Marstrand, Sweden (1998), Ponte de Lima, Portugal (2000), Dagstuhl, Germany (2002), Stirling, UK (2004, colocated with AMAST '04), Kuressaare, Estonia (2006, colocated with AMAST '06) and Marseille, France (2008). The 2010 conference will be held in Lac-Beauport, a suburb of Qu=E9bec City, Canada, and will be colocated with AMAST '10 (23-26 June 2010). INVITED SPEAKERS Roland Backhouse, University of Nottingham, UK. Others to be announced later. IMPORTANT DATES * Submission of abstracts: 7 December 2009 * Submission of full papers: 14 December 2009 * Notification of authors: 20 February 2010 * Camera-ready version: 20 March 2010 TOPICS Papers are solicited on mathematical methods and tools put to use in program construction. Topics of interest range from algorithmics to support for program construction in programming languages and systems. Some typical areas are type systems, program analysis and transformation, programming-language semantics, security and program logics. Theoretical contributions are welcome provided their relevance for program construction is clear. Reports on applications are welcome provided their mathematical basis is evident. SUBMISSION Submission is in two stages. Abstracts (plain text, 10 to 20 lines) must be submitted by 7 December 2009. Full papers (pdf) adhering to the LaTeX llncs style must be submitted by 14 December 2009. There is no official page limit, but authors should strive for brevity. The web-based system EasyChair will be used for submission (https://www.easychair.org/login.cgi?conf=3Dmpc2010). Papers must report previously unpublished work and not be submitted concurrently to another conference with refereed proceedings. In particular, they must not be submitted to AMAST 2010. Accepted papers must be presented at the conference by one of the authors. The proceedings of MPC'10 will be published in the Lecture Notes in Computer Science series of Springer-Verlag. After the conference, the authors of the best papers will be invited to submit revised versions to a special issue of the Science of Computer Programming journal of Elsevier. PROGRAMME COMMITTEE Jules Desharnais Universit=E9 Laval, Qu=E9bec, Canada (chair) Philippe Audebaud Ecole Normale Sup=E9rieure Lyon, France Ralph-Johan Back Abo Akademi University, Finland Eerke Boiten University of Kent, UK Sharon Curtis Oxford Brookes University, UK Jeremy Gibbons University of Oxford, UK Lindsay Groves Victoria University of Wellington, New Zealand Ian Hayes University of Queensland, Australia Eric Hehner University of Toronto, Canada Zhenjiang Hu National Institute of Informatics, Japan Johan Jeuring Utrecht University, Netherlands Christian Lengauer Universit=E4t Passau, Germany Bernhard M=F6ller Universit=E4t Augsburg, Germany Shin-Cheng Mu Academia Sinica, Taiwan David Naumann Stevens Institute of Technology, USA Jos=E9 Nuno Oliveira Universidade do Minho, Portugal Alberto Pardo Universidad de la Rep=FAblica, Uruguay Christine Paulin-Mohring INRIA-Universit=E9 Paris-Sud, France Steve Reeves University of Waikato, New Zealand Tim Sheard Portland State University, USA Georg Struth Sheffield University, UK Tarmo Uustalu Institute of Cybernetics, Estonia VENUE The conference will be held in the Manoir St-Castin (http://www.hotelsvillegia.com/villegia_stcastin/pages-eg/). This resort is located on the shore of Beauport lake, 15 minutes from downtown Qu=E9bec City (http://www.quebecregion.com/e/) and 15 minutes from the Jean-Lesage International Airport. LOCAL ORGANIZERS The local organizers are Claude Bolduc, Jules Desharnais and B=E9chir Kta= ri. Enquiries regarding the programme (submission, etc.) should be addressed to Jules.Desharnais@ift.ulaval.ca. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 14 20:50:50 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 14 Jul 2009 20:50:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MQrjK-0002um-CF for categories-list@mta.ca; Tue, 14 Jul 2009 20:48:14 -0300 Date: Tue, 14 Jul 2009 10:50:54 -0400 To: categories@mta.ca From: "Ellis D. Cooper" Subject: categories: Category Theory and So-Called Fundamental Results of Mathematics Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: "Ellis D. Cooper" Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 At http://en.wikipedia.org/wiki/Fundamental_theorem a "fundamental theorem" in a field of mathematics is defined to be "a theorem [or lemma] considered central to that field." The designation "fundamental" is often a matter of tradition, belonging to the history or sociology of mathematics. Some results, for example Hilbert's Nullstellensatz in algebraic geometry, are fundamental yet not generally designated "fundamental," although at http://en.wikipedia.org/wiki/Timeline_of_category_theory_and_related_mathematics it is indeed called that, along with a number of other results not called "fundamental" elsewhere. At http://en.wikipedia.org/wiki/Category:Fundamental_theorems there are links to articles on fundamental theorems of finitely generated abelian group, algebra, arithmetic, calculus, calculus of variations, combinatorial enumeration, curves, cyclic groups, Galois theory, homomorphisms, and linear algebra. To these can be added three "fundamental theorems of functional analysis" (Hahn-Banach, Open Mapping, Uniform Boundedness), the "fundamental theorem of Lie groups," and even a "fundamental theorem of fractal geometry" (Iterated Function System Convergence). Some of these results have been or can be revealingly stated if not yet proved in category theory terms (finitely generated abelian group, Galois theory, homomorphisms,...). My question is, what if any are the obstructions to extending this virtue to all of the so-called fundamental theorems? Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 16 13:20:04 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 16 Jul 2009 13:20:04 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MRTdb-0005RA-82 for categories-list@mta.ca; Thu, 16 Jul 2009 13:16:51 -0300 From: "Doering, Andreas" To: "categories@mta.ca" Date: Wed, 15 Jul 2009 09:21:32 +0100 Subject: categories: 5th CLP Workshop, August 6, 2009, Imperial College, London MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Doering, Andreas" Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 Dear all, we hereby wish to invite you to participate in the fifth workshop on "Categ= ories, Logic and Foundations of Physics" (CLP), which will take place at Imperial College on Thursday, 6th August 2009, 11:00 - 19:00, Lec= ture Theatre 2, Blackett Laboratory. REGISTRATION: As always, there is no formal registration, but for planning = reasons, please DO let us know via email if you will participate. Many than= ks! Travel information can be found here: http://www3.imperial.ac.uk/campusinfo= /southkensington Our workshop series is aimed at nourishing research in the fields named in = the title and at bringing together scientists from the different fields inv= olved. Please have a look at the website: http://categorieslogicphysics.wikidot.co= m/ The videos and slides of all the previous workshops plus a number of talks = from other events are online now. The site is constantly growing. SPEAKERS AND SCHEDULE: Confirmed speakers so far are: * Pedro Resende * Igor Bakovic * Paul Taylor * Leron Borsten * Aleks Kissinger There will be one more speaker. Please check the website for updates on the= schedule etc. Please bring the workshop to the attention of others who might be intereste= d. We are looking forward to seeing you (again) at "Categories, Logic and F= oundations of Physics". Best regards, Andreas Doering (Imperial) and Bob Coecke (Oxford) [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 17 12:02:58 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 17 Jul 2009 12:02:58 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MRovy-0003O6-F2 for categories-list@mta.ca; Fri, 17 Jul 2009 12:01:14 -0300 Date: Fri, 17 Jul 2009 12:39:06 +0100 (GMT Daylight Time) From: Eugenia Cheng To: categories@mta.ca Subject: categories: Hyland/Johnstone PSSL photos MIME-Version: 1.0 Content-Type: TEXT/PLAIN; FORMAT=flowed; CHARSET=US-ASCII Sender: categories@mta.ca Precedence: bulk Reply-To: Eugenia Cheng Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 Dear All, Photos are now available from the PSSL in honour of Martin Hyland and Peter Johnstone in April. Thanks are due to Juergen Koslowski for his wonderful photos. If you can help supply a few of the missing names on the individual photos, or if you spot any errors, please do email me. The photos can be accessed from the main PSSL page, along with slides from the talks, and a brief write-up of the weekend. If you would like to add any more photos to the record of the weekend, please email me. PSSL page: http://cheng.staff.shef.ac.uk/pssl88/ I would like to thank everyone once again for making the weekend so memorable. Best wishes, Eugenia [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Sun Jul 19 15:42:15 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 19 Jul 2009 15:42:15 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MSbI8-0000sF-IP for categories-list@mta.ca; Sun, 19 Jul 2009 15:39:20 -0300 From: Jean-Yves Marion To: Jean-Yves Marion Subject: categories: Stacs 2010 Mime-Version: 1.0 (Apple Message framework v935.3) Date: Sun, 19 Jul 2009 11:37:53 +0200 Content-Type: text/plain;charset=ISO-8859-1;format=flowed;delsp=yes Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Jean-Yves Marion Message-Id: Status: O X-Status: X-Keywords: X-UID: 22 ************************************************************************ 27th International Symposium on Theoretical Aspects of Computer Science STACS 2010 - CALL FOR PAPERS MARCH 4-6, 2010, NANCY, FRANCE http://stacs.loria.fr/ ************************************************************************ SCOPE ******** Authors are invited to submit papers presenting original and unpublished research on theoretical aspects of computer science. Typical areas include (but are not limited to): * Algorithms and data structures, including: parallel and distributed =20= algorithms, computational geometry, cryptography, algorithmic learning theory; * Automata and formal languages; * Computational and structural complexity; * Logic in computer science, including: semantics, specification, and verification of programs, rewriting and deduction; * Current challenges, for example: biological computing, quantum computing, mobile and net computing. INVITED SPEAKERS *********************** Mikolaj Bojanczyk, Warsaw University Rolf Niedermeier, University of Jena Jacques Stern, Ecole Normale Sup=E9rieure PROGRAM COMMITTEE *************************** Markus Bl=E4ser, Saarland University Harry Buhrman, CWI, University of Amsterdam Thomas Colcombet, CNRS, Paris 7 University Anuj Dawar, University of Cambridge Arnaud Durand, Paris 7 University S=E1ndor Fekete, Braunschweig University of Technology Ralf Klasing, CNRS, Bordeaux University Christian Knauer, Freie Universit=E4t of Berlin Piotr Krysta, University of Liverpool Sylvain Lombardy, Marne la Vall=E9e University Parthasarathy Madhusudan, University of Illinois Jean-Yves Marion, Nancy University (co-chair) Pierre McKenzie, Universit=E9 de Montr=E9al Rasmus Pagh, IT University of Copenhagen Boaz Patt-Shamir, Tel Aviv University Christophe Paul, CNRS, Montpellier University Georg Schnitger, Frankfurt University Thomas Schwentick, TU Dortmund University (co-chair) Helmut Seidl, TU Munich Jir=ED Sgall, Charles University Sebastiano Vigna, Universit=E0 degli Studi di Milano Paul Vitanyi, CWI, Amsterdam SUBMISSIONS ******************* Authors are invited to submit a draft of a full paper with at most 12 pages (STACS style or similar - e.g. LaTeX article style, 11pt a4paper). The title page must contain a classification of the topic covered, preferably using the list of topics above. The paper should contain a succinct statement of the issues and of their motivation, a summary of the main results, and a brief explanation of their significance, accessible to non-specialist readers. Proofs omitted due to space constraints must be put into an appendix to be read by the program committee members at their discretion. Submissions deviating from these guidelines risk rejection. Electronic submissions should be formatted in PostScript or PDF.Simultaneous submission to other conferences with published proceedings is not allowed. PROCEEDINGS ******************** Accepted papers will appear in the proceedings of the Symposium, which =20= are published electronically in the LIPIcs (Leibniz International Proceedings in Informatics) series, available =20 through Dagstuhl's website. The LIPIcs series provides an ISBN for the proceedings volume and =20 manages the indexing issues. Accepted papers will also be archived in the open access electronic =20 repositories HAL and arXiv. These gateways, as well as the LIPIcs series, guarantee perennial, =20 free and easy electronic access, while the authors will retain the rights over their work. With their submission, authors consent to sign a license authorizing =20 the program committee chairs to organize the electronic publication of their paper if it is accepted. Further details are available on www.stacs-conf.org and on the =20 conference website. Participants of the conference will receive a printed version of the =20 proceedings. It is also planned to publish in a journal a selection of papers. IMPORTANT DATES *************************** Deadline for submission: September 22, 2009 Notification to authors: November 26, 2009 Final version: December 18, 2009 Symposium: March 4-6, 2010= [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Mon Jul 20 09:29:26 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 20 Jul 2009 09:29:26 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MSry7-00078x-GZ for categories-list@mta.ca; Mon, 20 Jul 2009 09:27:47 -0300 Date: Mon, 20 Jul 2009 01:01:42 +0200 Subject: categories: Existence of very high categories From: Rafael Borowiecki To: categories@mta.ca Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Rafael Borowiecki Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 Hi all Note my new e-mail. I had to get a new e-mail to exclude html. I am not an expert on oo-categories but i am sure there is a structure to the "class" of all omega-categories. I hope all this will not depend on the definition of an oo-category. 6> Is the "class" of oo-categories of a certain recursive depth always an oo-category of depth one higher than the previous depth? I think yes for both strict and weak oo-categories. What should the "class" of all n-categories in Makkais foundation be called to describe it technically accurately? An oo-cosmos? in the categorical sense of a cosmos. I am not sure but this "class" maby also contain all oo-categories. Are there different strict/weak n-categories with n any infinite ordinal number omega? omega does remind of an ordinal number. The category need not to be accessible by forming categories of categories, just satisfy some axioms of an strict/weak oo-category for oo=omega. There might be a better definition of an omega-category if it is necessary at all, i don't know. Best regards Rafael Borowiecki [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Mon Jul 20 19:33:22 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 20 Jul 2009 19:33:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MT1N1-0006Cm-DM for categories-list@mta.ca; Mon, 20 Jul 2009 19:30:07 -0300 Date: Mon, 20 Jul 2009 16:03:04 +0200 From: Andree Ehresmann To: Rafael Borowiecki , categories@mta.ca Subject: categories: Re: Existence of very high categories MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Andree Ehresmann Message-Id: Status: O X-Status: X-Keywords: X-UID: 24 A partial answer to Rafael Borowiecki's question about the class of =20 n-categories is given in a 30 years old paper I had published with =20 Charles Ehresmann: "Multiple categories, II: The monoidal closed category of multiple =20 categories", Cahiers de Top. et GD XIX-3 (1978), 295-333. Il is freely =20 accessible on the NUMDAM =20 site:http://archive.numdam.org/ARCHIVE/CTGDC/CTGDC_1978__19_3/CTGDC_1978__19= _3_295_0/CTGDC_1978__19_3_295_0.pdf Andr=E9e [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Wed Jul 22 14:02:27 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 22 Jul 2009 14:02:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MTf9G-0005ro-9Z for categories-list@mta.ca; Wed, 22 Jul 2009 13:58:34 -0300 MIME-Version: 1.0 Date: Tue, 21 Jul 2009 11:41:30 +0200 Subject: categories: Re: Existence of very high categories From: Urs Schreiber To: Rafael Borowiecki , categories@mta.ca Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Urs Schreiber Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 Rafael Borowiecki wrote: > I am not an expert on oo-categories but i am sure there is a structure to > the "class" of all omega-categories. I hope all this will not depend on the > definition of an oo-category. Given any notion of higher category, usually considerable interesting information is already encoded in the collection of all of these - with all suitable morphisms between them - and with all suitable invertible transformations and invertible higher transformations between these. Notably this is sufficient to talk about equivalence of the higher categories in question. In other words, given any notion of higher category, their collection should at least form an (oo,1)-category. http://ncatlab.org/nlab/show/%28infinity%2C1%29-category This should be the truncation of a more general structure, but should already contain a considerable amount of the relevant information and structure. For various flavors of higher categories the corresponding (oo,1)-categories "of all of them" are well known. These are "presented" by what is known as "folk model structures": http://ncatlab.org/nlab/show/folk+model+structure . More generally and more recently, Jacob Lurie has used unpublished work by Clark Barwick to define and study (oo,1)-categories of collections of (infty,n)-categories for n in N http://ncatlab.org/nlab/show/(infinity,n)-category > Are there different strict/weak n-categories with n any infinite > ordinal number omega? > omega does remind of an ordinal number. One should beware that in practice the difference between the usage "oo-category" and "omega-category" is usually more due to tradition than being of intrinsic meaning. Ross Street originally introduced "omega-category" to explicitly denote a notion where cells of non-finite degree exist, but later authors didn't stick to that use of the work. Compare the remark by Sjoerd Crans that is reproduced here: http://ncatlab.org/nlab/show/strict+omega-category [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Wed Jul 22 14:02:27 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 22 Jul 2009 14:02:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MTf8E-0005n4-RU for categories-list@mta.ca; Wed, 22 Jul 2009 13:57:30 -0300 Date: Tue, 21 Jul 2009 09:11:02 +0200 From: =?ISO-8859-1?Q?Jean-Christophe_Filli=E2tre?= MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Call for Papers: PLPV 2010 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: =?ISO-8859-1?Q?Jean-Christophe_Filli=E2tre?= Message-Id: Status: O X-Status: X-Keywords: X-UID: 26 Call For Papers Programming Languages meets Program Verification (PLPV) 2010 http://slang.soe.ucsc.edu/plpv10/ Tuesday, January 19, 2010 Madrid, Spain Affiliated with POPL 2010 Overview: The goal of PLPV is to foster and stimulate research at the intersection of programming languages and program verification. Work in this area typically attempts to reduce the burden of program verification by taking advantage of particular semantic and/or structural properties of the programming language. One example is dependently typed programming languages, which leverage a language's type system to specify and check richer than usual specifications, possibly with programmer-provided proof terms. Another example is extended static checking systems like Spec#, which extends C# with pre- and postconditions along with a static verifier for these contracts. We invite submissions on all aspects, both theoretical and practical, of the integration of programming language and program verification technology. To encourage cross-pollination between different communities, we seek a broad the scope for PLPV. In particular, submissions may have diverse foundations for verification (type-based, Hoare-logic-based, etc), target diverse kinds of programming languages (functional, imperative, object-oriented, etc), and apply to diverse kinds of program properties (data structure invariants, security properties, temporal protocols, etc). Submissions: Submissions should fall into one of the following three categories: 1. Regular research papers that describe new work on the above or related topics. Submissions in this category have an upper limit of 12 pages, but shorter submissions are also encouraged. 2. Work-in-progress reports should describe new work that is ongoing and may not be fully completed or evaluated. Submissions in this category should be at most 6 pages in total length. 3. Proposals for challenge problems which the author believes is are useful benchmarks or important domains for language-based program verification techniques. Submissions in this category should be at most 6 pages in total length. Submissions should be prepared with SIGPLAN two-column conference format. Submitted papers must adhere to the SIGPLAN republication policy. Concurrent submissions to other workshops, conferences, journals, or similar forums of publication are not allowed. Publication: Accepted papers will be published by the ACM and appear in the ACM digital library. Student Attendees: Students with accepted papers or posters are encouraged to apply for a SIGPLAN PAC grant that will help to cover travel expenses to PLPV. Details on the PAC program and the application can be found on the workshop web page. PAC also offers support for companion travel. Important Dates: * Electronic submission: October 8, 2009, 11:59pm Samoa time (UTC-11) * Notification: November 8, 2009 * Final version: November 17, 2009 * Workshop: January 19, 2010 Organizers: * Cormac Flanagan (University of California, Santa Cruz) * Jean-Christophe Filli=E2tre (CNRS) Program Committee: * Adam Chlipala (Harvard University) * Ranjit Jhala (University of California, San Diego) * Joseph Kiniry (University College Dublin) * Rustan Leino (Microsoft Research) * Xavier Leroy (INRIA Paris-Rocquencourt) * Conor McBride (University of Strathclyde) * Andrey Rybalchenko (Max Planck Institute for Software Systems) * Tim Sheard (Portland State University) * Stephanie Weirich (University of Pennsylvania) [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 24 16:13:41 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Jul 2009 16:13:41 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MUQAX-0005pY-CZ for categories-list@mta.ca; Fri, 24 Jul 2009 16:11:01 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Transfer-Encoding: 7bit From: Marco Grandis Subject: categories: CT2010 Date: Fri, 24 Jul 2009 15:17:18 +0200 To: categories@mta.ca Sender: categories@mta.ca Precedence: bulk Reply-To: Marco Grandis Message-Id: Status: RO X-Status: X-Keywords: X-UID: 27 CT2010 Dear colleagues, as announced at CT2009, in Cape Town, the next International Category Theory meeting will take place in Genoa. It will take place from Sunday, 20 June, to Saturday, 26 June 2010. Looking forward to your participation the organisers Marco Grandis, Sandra Mantovani, Eugenio Moggi, Giuseppe Rosolini, Robert Walters [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Mon Jul 27 18:01:12 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Jul 2009 18:01:12 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVXGk-0005Pw-Ag for categories-list@mta.ca; Mon, 27 Jul 2009 17:58:02 -0300 MIME-Version: 1.0 Date: Mon, 27 Jul 2009 14:10:28 +0200 Subject: categories: Call for participation: Computability and complexity in analysis 2009 From: Andrej Bauer To: constructivenews@googlegroups.com, categories list Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Andrej Bauer Message-Id: Status: O X-Status: X-Keywords: X-UID: 28 ______________________________________________________________ Call for Participation Sixth International Conference on Computability and Complexity in Analysis 2009 (CCA 2009) August 18-22, 2009, Ljubljana, Slovenia Early registration deadline: July 31, 2009 ______________________________________________________________ Invited Speakers * Mark Braverman (Cambridge, USA) * Vladik Kreinovich (El Paso, USA) * Dana Scott (Pittsburgh, USA) * Ning Zhong (Cincinnati, USA) Scientific Program Committee * Andrej Bauer (Ljubljana, Slovenia) * Vasco Brattka (Cape Town, South Africa) * Mark Braverman (Cambridge, USA) * Pieter Collins (Amsterdam, The Netherlands) * Peter Hertling, co-chair (Munich, Germany) * Hajime Ishihara (Ishikawa, Japan) * Ker-I Ko, co-chair (Stony Brook, USA) * Robert Rettinger (Hagen, Germany) * Victor Selivanov (Novosibirsk, Russia) * Alex Simpson (Edinburgh, Great Britain) * Dieter Spreen (Siegen, Germany) * Frank Stephan (Singapore) * Xizhong Zheng (Glenside, USA) Organizing Committee * Andrej Bauer, chair (Ljubljana, Slovenia) * Iztok Kavkler (Ljubljana, Slovenia) * Davorin Le=C5=A1nik (Ljubljana, Slovenia) * Matija Pretnar (Ljubljana, Slovenia) Tutorials * Mart=C3=ADn Escard=C3=B3 (Birmingham, UK) * Bas Spitters and Russell O'Connor (Eindhoven, The Netherlands) Venue Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics, and Mechanics, Slovenia Registration Fees * Euro 100 until July 31, 2009 (standard fee) * Euro 120 after July 31, 2009 (late fee) Schedule The tentative schedule as well as further information on registration, accommodation, and traveling is available here: http://cca.fmf.uni-lj.si/ Proceedings Accepted papers will be published in an electronic proceedings volume in the DROPS series of Schloss Dagstuhl. In addition, a technical report containing the accepted papers will be available at the conference. It is planned to publish a special issue of some journal dedicated to CCA 2009 after the conference. Conference Web Page http://cca-net.de/cca2009/ ______________________________________________________________ [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Mon Jul 27 18:01:12 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Jul 2009 18:01:12 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVXIQ-0005XO-Br for categories-list@mta.ca; Mon, 27 Jul 2009 17:59:46 -0300 MIME-Version: 1.0 Date: Mon, 27 Jul 2009 14:45:38 +0200 Subject: categories: Sheaf toposes and chain-complete posets From: Andrej Bauer To: categories list Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Andrej Bauer Message-Id: Status: O X-Status: X-Keywords: X-UID: 29 Dear categorists, I am trying to wrap my mind around the concept of an (internal) chain-complete poset in a sheaf topos. I am failing to come up with an example of a poset that is chain-complete but is not complete. The precise definitions of "chain-complete" in the internal language are as follows. Suppose (P, <=) is a poset in a topos. For C in Omega^P, let chain(C) be the statement forall x, y : P, (x in C and y in C) ==> (x <= y or y <= x) Then P is chain-complete if forall C : Omega^P, chain(C) ==> exists x : P, x is the supremum of C where "x is the supremum of C" means the usual thing. So what does a chain-complete poset which isn't complete look like? Since I am used to arguing intuitionistically, it would help a lot if there were some (possibly infinitary) logical principle or schema that is typical of sheaf toposes -- something expressing the local nature of validity. Such a principle ought to be invalid in realizability toposes, so perhaps it should express or imply cocompleteness (with respect to Set). But would that be of any help for arguing in the internal language? With kind regards, Andrej Bauer [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 14:08:09 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:08:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVq9I-0000dJ-EI for categories-list@mta.ca; Tue, 28 Jul 2009 14:07:36 -0300 Date: Tue, 28 Jul 2009 00:06:21 -0400 From: "Fred E.J. Linton" To: Subject: categories: Re: Sheaf toposes and chain-complete posets Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Fred E.J. Linton" Message-Id: Status: O X-Status: X-Keywords: X-UID: 30 On Mon, 27 Jul 2009 05:05:59 PM EDT, Andrej Bauer asked: > So what does a chain-complete poset which isn't complete look like? Take the product of any nonempty discrete poset X with the ordinal 2. Give Xx2 the "product order" ((x, a) Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:08:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVq7o-0000Vp-0x for categories-list@mta.ca; Tue, 28 Jul 2009 14:06:04 -0300 From: Pedro Resende To: Categories list Content-Type: text/plain; charset=ISO-8859-1; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable Mime-Version: 1.0 (Apple Message framework v935.3) Subject: categories: Postdoctoral Positions 2010/2011 Date: Tue, 28 Jul 2009 00:16:55 +0100 Sender: categories@mta.ca Precedence: bulk Reply-To: Pedro Resende Message-Id: Status: O X-Status: X-Keywords: X-UID: 31 Dear colleagues, The announcement below may be of interest to readers of the categories =20= list. Please note that the new application deadline (December 1, 2009) =20= is different from the usual one. Best regards, Pedro ######### Postdoctoral Positions 2010/2011 The Center for Mathematical Analysis, Geometry, and Dynamical Systems =20= of the Department of Mathematics of Instituto Superior T=E9cnico, =20 Lisbon, Portugal, invites applications for postdoctoral positions for =20= research in mathematics, subject to budgetary approval. Positions are =20= for one year, with the possibility of extension for a second year upon =20= mutual agreement. Selected candidates will be able to take up their =20 position between September 1, 2010, and January 1, 2011. Applicants should have a Ph.D. in mathematics, or in a related area =20 relevant to the scientific interests of the faculty of the Center, =20 preferably obtained after December 31, 2007. They must show very =20 strong research promise in one of the areas in which the faculty of =20 the Center is currently active. There are no teaching duties =20 associated with these positions. Applicants should send a curriculum vitae; reprints, preprints and/or =20= dissertation abstract; description of research project (of no more =20 than 1,000 words); and ask that three letters of reference are sent =20 directly to the director: Prof. Carlos Rocha Center for Mathematical Analysis, Geometry, and Dynamical Systems Departamento de Matem=E1tica Instituto Superior T=E9cnico Avenida Rovisco Pais 1049-001 Lisboa Portugal. To ensure full consideration, complete application packages(*) should =20= be received by December 1, 2009. Additional information about the =20 Center and the positions is available at http://camgsd.math.ist.utl.pt/. (*) Please note that materials sent by email will not be considered.= [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 14:08:29 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:08:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVqA3-0000hv-07 for categories-list@mta.ca; Tue, 28 Jul 2009 14:08:23 -0300 MIME-Version: 1.0 Date: Tue, 28 Jul 2009 07:44:31 +0200 Subject: categories: Re: Sheaf toposes and chain-complete posets From: Andrej Bauer To: categories list Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Andrej Bauer Message-Id: Status: O X-Status: X-Keywords: X-UID: 32 Dear categorists, I should have asked a different question: what does a chain-complete _lattice_ which is not complete look like in a sheaf topos? Is there such a thing? (Thanks to Fred Linton who pointed out that I could just take a flat order and multiply it with a complete one, thus gettting a poset which has very few interesting chains but is not at all complete.) With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 14:09:42 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:09:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVqBC-0000qO-Vp for categories-list@mta.ca; Tue, 28 Jul 2009 14:09:35 -0300 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Sam Staton Subject: categories: Re: Sheaf toposes and chain-complete posets Date: Tue, 28 Jul 2009 09:35:55 +0100 To: Andrej Bauer , Sender: categories@mta.ca Precedence: bulk Reply-To: Sam Staton Message-Id: Status: O X-Status: X-Keywords: X-UID: 33 Dear Andrej, when you say "complete" but not "chain-complete", do you mean "directed complete"? Here is (I think) an example that is also natural and relevant. Do you know Andy Pitts' work (with others) on Nominal Sets? The category of nominal sets is a sheaf topos (the "Schanuel topos", it is actually Boolean). Andy has done some domain theory in nominal sets to model a language with dynamic allocation of fresh names, FreshML. Fixing an infinite set of "atoms" A, then the category of nominal sets is a subcategory of the category of actions of the symmetric group on A (see reference for full definition). The set of atoms has itself a natural group action. The finite powerset of the nominal set of atoms, ordered by inclusion, is chain complete, but not directed complete. Any chain of finite sets can only have finite support, and is thus necessarily finite. But the full finite powerset is itself directed, without an upper bound. I hope that is of some help. Best regards, Sam. Reference: Section 3 of On a Monadic Semantics for Freshness, M. R. Shinwell and A. M. Pitts, Theoretical Computer Science 342, 2005. Available from Andy Pitts' web page. NB "nominal sets" are there called "FM-sets". The example I mention appears in Mark Shinwell's PhD thesis, The Fresh Approach: functional programming with names and binders. http:// www.cl.cam.ac.uk/techreports/UCAM-CL-TR-618.html. On 27 Jul 2009, at 13:45, Andrej Bauer wrote: > Dear categorists, > > I am trying to wrap my mind around the concept of an (internal) > chain-complete poset in a sheaf topos. I am failing to come up with an > example of a poset that is chain-complete but is not complete. The > precise definitions of "chain-complete" in the internal language are > as follows. > > Suppose (P, <=) is a poset in a topos. For C in Omega^P, let chain(C) > be the statement > > forall x, y : P, (x in C and y in C) ==> (x <= y or y <= x) > > Then P is chain-complete if > > forall C : Omega^P, chain(C) ==> exists x : P, x is the supremum > of C > > where "x is the supremum of C" means the usual thing. > > So what does a chain-complete poset which isn't complete look like? > > Since I am used to arguing intuitionistically, it would help a lot if > there were some (possibly infinitary) logical principle or schema that > is typical of sheaf toposes -- something expressing the local nature > of validity. Such a principle ought to be invalid in realizability > toposes, so perhaps it should express or imply cocompleteness (with > respect to Set). But would that be of any help for arguing in the > internal language? > > With kind regards, > > Andrej Bauer > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 14:10:14 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:10:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVqBk-0000tp-Ji for categories-list@mta.ca; Tue, 28 Jul 2009 14:10:08 -0300 To: categories@mta.ca Subject: categories: FICS'09 Call for participation - Fixed Points in Computer Science (CSL'09 workshop) Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Date: Tue, 28 Jul 2009 16:19:05 +0300 From: Tarmo Uustalu Sender: categories@mta.ca Precedence: bulk Reply-To: Tarmo Uustalu Message-Id: Status: RO X-Status: X-Keywords: X-UID: 34 Call for Participation 6th Workshop on Fixed Points in Computer Science, FICS 2009 Coimbra, Portugal, 12-13 September 2009, a satellite workshop of CSL 2009, colocated with PPDP 2009, LOPSTR 2009 http://cs.ioc.ee/fics09/ Background Fixed points play a fundamental role in several areas of computer science and logic by justifying induction and recursive definitions. The construction and properties of fixed points have been investigated in many different frameworks such as: design and implementation of programming languages, program logics, databases. The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science and logic communities who study or apply the theory of fixed points. Previous workshops where held in Brno (1998, MFCS/CSL workshop), Paris (2000, LC workshop), Florence (2001, PLI workshop), Copenhagen (2002, LICS (FLoC) workshop), Warsaw (2003, ETAPS workshop). Topics for the call for papers included, but were not restricted to: * categorical, metric and ordered fixed point models * fixed points in algebra and coalgebra * fixed points in languages and automata * fixed points in programming language semantics * the mu-calculus and fixed points in modal logic * fixed points in process algebras and process calculi * fixed points in the lambda-calculus, = functional programming and type theory * fixed points in relation to dataflow and circuits * fixed points in logic programming and theorem proving * finite model theory, descriptive complexity theory, = fixed points in databases Invited speakers Robin Cockett (University of Calgary) Javier Esparza (Technische Universit=E4t M=FCnchen) Yde Venema (Universiteit van Amsterdam) Contributed talks Loredana Afanasiev and Balder ten Cate On core XPath with inflationary fixed points Lars Birkedal, Kristian St=F8vring and Jacob Thamsborg Solutions of generalized recursive metric-space equations Pierre Clairambault Least and greatest fixpoints in game semantics Zolt=E1n =C9sik and Stephen L. Bloom Scattered algebraic linear orderings Stephan Kreutzer and Martin Lange A note on the relation between inflationary fixpoints and = least fixpoints of higher order Omer Landry Nguena Timo and Pierre-Alain Reynier On characteristic formulae for event-recording automata Robert Myers Regular expressions and the coalgebraic mu-calculus Milad Niqui and Jan Rutten Coinductive predicates as final coalgebras Pawel Parys Lower bound for evaluation of mu-nu fixpoint Dulma Rodriguez and Martin Hofmann Membership checking in greatest fixpoints revisited Daniel Stamate A bilattice based fixed point semantics for integrating imperfect = information Kohtaro Tadaki Fixed points on partial randomness Yoshinori Tanabe and Masami Hagiya Fixed-point computations over functions on integers with operations = min, max and plus Balder ten Cate and Gaelle Fontaine An easy completeness proof for the modal mu-calculus on finite trees Lionel Vaux A non-uniform finitary relational semantics of system T Programme committee Yves Bertot (INRIA Sophia Antipolis) Anuj Dawar (University of Cambridge) Peter Dybjer (Chalmers University of Technology) Zolt=E1n =C9sik (University of Szeged) Masahito Hasegawa (Kyoto University) Anna Ing=F3lfsd=F3ttir (Reykjavik University) Ralph Matthes (IRIT, Toulouse) (co-chair) Jan Rutten (CWI and Vrije Universiteit Amsterdam) Luigi Santocanale (LIF, Marseille) Alex Simpson (University of Edinburgh) Tarmo Uustalu (Institute of Cybernetics, Tallinn) (co-chair) Igor Walukiewicz (LaBRI, Bordeaux) Registration and cost Registration is through the CSL/PPDP/LOPSTR website. The FICS participation fee of 80 EUR includes 4 coffee breaks and the = workshop dinner on Saturday. All workshop participants will = receive a copy of the informal workshop proceedings. The early registration deadline for the CSL/PPDP/LOPSTR main conferences is 31 July. For FICS, there is no early/late rate difference. Sponsors EXCS, Estonian Centre of Excellence in Computer Science [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 14:15:30 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 14:15:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVqGe-0001Ml-B0 for categories-list@mta.ca; Tue, 28 Jul 2009 14:15:12 -0300 Date: Tue, 28 Jul 2009 16:09:56 +0000 (GMT) From: RONALD BROWN Subject: categories: 2 new presentations To: categories list MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: RONALD BROWN Message-Id: Status: O X-Status: X-Keywords: X-UID: 36 I have made pdf files of two recent presentations available from =0A=0Aww= w.bangor.ac.uk/r.brown/askloster.html=0A=0ASome intuitions of higher dimens= ional algebra, and potential applications=0A=0ACategory theory, higher dime= nsional algebra, groupoid atlases: prospective=0Adescriptive tools in theor= etical neuroscience=0A=0ARonnie [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Tue Jul 28 18:29:54 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jul 2009 18:29:54 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MVuCm-0005jT-4U for categories-list@mta.ca; Tue, 28 Jul 2009 18:27:28 -0300 Date: Tue, 28 Jul 2009 13:36:54 -0500 (CDT) From: Zhaohua Luo Subject: categories: Paper available: Clone Theory and Algebraic Logic To: categories MIME-version: 1.0 Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Zhaohua Luo Message-Id: Status: O X-Status: X-Keywords: X-UID: 37 The paper "Clone Theory and Algebraic Logic" is available at http://www.algebraic.net/ctal The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right algebras over a clone are covariant and contravariant functors from the category to that of sets respectively. In this paper we show that first-order logic can be studied effectively using the notions of right and left algebras over a clone. It is easy to translate the classical treatment of logic into our setting and prove all the fundamental theorems of first-order theory algebraically. Zhaohua Luo [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Wed Jul 29 11:34:52 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 29 Jul 2009 11:34:52 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MWAC2-0001Wf-Sr for categories-list@mta.ca; Wed, 29 Jul 2009 11:31:46 -0300 Date: Tue, 28 Jul 2009 21:38:28 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: (Pre)prints MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: O X-Status: X-Keywords: X-UID: 38 I would like to call your attention to three relatively new items on my ftp site, all joint with John Kennison and Bob Raphael: Local extension of maps, Isbell duality, Isbell duality for modules. To see them, simply browse to ftp.math.mcgill.ca/pub/barr/pdffiles and click on Index.html. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Thu Jul 30 10:32:47 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 30 Jul 2009 10:32:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MWViu-00048b-JZ for categories-list@mta.ca; Thu, 30 Jul 2009 10:31:08 -0300 Date: Thu, 30 Jul 2009 10:56:42 +0200 From: Andre.Rodin@ens.fr To: categories@mta.ca Subject: categories: preprint: Categories without structures MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Sender: categories@mta.ca Precedence: bulk Reply-To: Andre.Rodin@ens.fr Message-Id: Status: RO X-Status: X-Keywords: X-UID: 39 Dear all, I would like to announce this recent preprint of mine: http://arxiv.org/abs/0907.5143 Title: Categories without structures Abstract: The popular view according to which Category theory provides a = support for Mathematical Structuralism is erroneous. Category-theoretic foundatio= ns of mathematics require a different philosophy of mathematics. While structur= al mathematics studies "invariant forms" (Awodey) categorical mathematics st= udies covariant transformations which, generally, don't have any invariants. In= this paper I develop a non-structuralist interpretation of categorical mathema= tics and show its consequences for history of mathematics and mathematics educ= ation. Andrei [For admin and other information see: http://www.mta.ca/~cat-dist/ ] From rrosebru@mta.ca Fri Jul 31 14:28:38 2009 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 31 Jul 2009 14:28:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MWvrl-00057T-5G for categories-list@mta.ca; Fri, 31 Jul 2009 14:26:01 -0300 Date: Fri, 31 Jul 2009 10:53:02 +0900 From: Hitoshi Ohsaki (RTA publicity chair) To: categories@mta.ca Subject: categories: FLoC 2010: Call For Workshops Deadline Extension Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Hitoshi Ohsaki (RTA publicity chair) Message-Id: Status: O X-Status: X-Keywords: X-UID: 40 FLoC 2010: Call For Workshops Deadline Extension: Workshop proposals can now be submitted up to Sept. 1, 2009. The original Call for Workshops is at http://www.floc-conference.org/cfw.html . Organizers will be notified by October 15, 2009. Proposals should be submitted electronically to EasyChair at the following address: http://www.easychair.org/conferences/?conf=floc10cfw (Clearly indicate at the top of the proposal the relevant conference) For further enquiries or information, please contact: Philip Scott (FLoC Workshop Chair) Department of Mathematics and Statistics University of Ottawa Ottawa, Ont. Canada K1N 6N5 email: phil@site.uottawa.ca [For admin and other information see: http://www.mta.ca/~cat-dist/ ]