Subj: ftp paper Date: Wed, 12 Aug 92 14:47:57 EDT From: cubric@triples.Math.McGill.CA (Djordje Cubric) I would like to announce that the draft of my paper "On Free CCC" is available from ftp triples.math.mcgill.ca. The paper contains a proof of the following: Theorem: Let C be a free cartesian closed category. Then there exists a faithful structure preserving functor F:C->Set. Isn't this just the H. Friedman's completeness result for the typed lambda calculus? NO. One has also to show that in the free cartesian closed category all the arrows into the terminal object are epi. We prove the result using Mints' reductions (but with a repaired proof). Along the way we conclude also that: Mints reductions are weakly normalizing, the strategy being: first do all eta-like expansions (with the restrictions) and then beta-like reductions. To get the file (if you can read ps files) do: ftp triples.math.mcgill.ca Name: anonymous Password: "your e-mail address" >cd pub/cubric >binary >get frccc.ps >quit If you can't read ps files there are also frccc.dvi and frccc.tex (which needs Barr's diagram.tex macros and they are at the same ftp site except under pub/texmacros). In case of any problems I'll gladly send you a copy by regular mail. Any comments are welcome. Djordje Cubric ============================================================================== Subj: October Meeting Date: Thu, 13 Aug 92 08:30:51 EDT From: fox@triples.Math.McGill.CA (Thomas F. Fox) CATEGORY THEORY MEETING: OCT 10-11, 1992 CATEGORY THEORY RESEARCH CENTER, MCGILL UNIVERSITY, MONTREAL Dear Colleague, We look forward to seeing you again this fall. We will meet in the basement of Burnside Hall (805 Sherbrooke St W) at 9:00 Saturday morning for coffee, and the first talk will be at 9:30. If you wish to speak, please contact Michael Barr as soon as possible. A final list of speakers will be drawn up Saturday morning. Below you will find a list of hotels and tourist rooms within easy walking distance of McGill. You should mention McGill when making your reservation to obtain the quoted price. If you have any further questions, contact Tom Fox. Hotels: L'Appartement, 455 Sherbrooke W, 284-3634, $82.50 Howard Johnson Plaza, 475 Sherbrooke W, 842-3961, $79 Citadelle, 410 Sherbrooke W, 844-8851, $84.50 Delta, 475 President Kennedy, 289-1986, $89 Four Seasons, 1050 Sherbrooke W, 284-1110, $140 Holiday Inn, 420 Sherbrooke W, 842-6111, $94 Journey's End, 3440 Park Ave, 849-1413, $75-85 Hotel du Parc, 3625 Park Ave, 288-6666, $90 Versailles*, 1659 Sherbrooke W, 933-3611, $89 Tourist Rooms: Ambrose, 3422 Stanley, 288-6922, $45-50 Armor*, 151 Sherbrooke E, 285-0140, $32-59 Casa Bella, 258 Sherbrooke W, 849-2777, $39-75 Pierre*, 169 Sherbrooke E, 288-8519, $35-55 *20 minute walk from McGill Michael Barr barr@triples.math.mcgill.ca Tom Fox fox@triples.math.mcgill.ca ============================================================================== Subj: Geometric or coherent logic? Date: Tue, 18 Aug 92 16:04:15 From: sjv (Steve Vickers)@doc.ic.ac.uk I've become accustomed to referring to - - coherent logic, with connectives true, /\, false, \/, = and (exists); and - geometric logic that also admits infinitary \/. I think I got this sense of "geometric" from Mike Fourman, and then "coherent" is natural because coherent theories are classified by coherent toposes. But the published works vary considerably. In particular, where I have coherent geometric, Makkai and Reyes have finitary coherent coherent, Johnstone has finitary geometric generalized geometric MacLane and Moerdijk have geometric (not referred to). Is usage as chaotic as it appears? Steve Vickers. ============================================================================== Subj: From Jurgen Koslowski Date: Wed, 19 Aug 92 16:16:37 CDT From: koslowj@math.ksu.edu (Juergen Koslowski) The time seems to have come to bid farewell to the mathematics community as a whole, and to category theorists in particular. It has been a privilege for the last 10 years to be able to work in this very special area of mathematics. Although I did receive a last minute job offer earlier this month from an U.S. University, after agonizing negotiations the terms of this offer turned out to be insufficient to procced with an application for the "green card". After having had an H-1 visa for 6 years, a further extension was not possible either. My present H-1 visa expires on August 31, which gives me until the end of September (I guess) to leave the U.S. and return to Germany. If anybody knows of a position that might be available on (very) short notice, please contact me immediately by email koslowj@math.ksu.edu or koslowj@cis.ksu.edu A position in the U.S. would have to be a "tenured or tenure track or a permanent research position". If I am forced to move back to Germany I will post a mailing address. I would appreciate it if you could keep me on your mailing lists for pre-prints, although at the moment I do not know whether I can stay involved in mathematics professionally. Thank you all very much for making these last 10 years worthwhile! -- J"urgen Koslowski ============================================================================== Subj: Geometric or coherent logic? Date: Sun, 23 Aug 92 22:28:46 EDT From: MT78000 This is Michael Makkai replying to Steve Vickers' query on coherent vs geometric logic. Despite the variety you found in the literature, I think you are right about the standard usage. I certainly have used the terms in those senses now for a long time (despite what appears in Makkai/Reyes). I think Andy Pitts will agree with me; in fact I vaguely recall that I told myself at one point that I would observe Pitts' usage in this respect. ============================================================================== Subj: Linear Algebra Date: Fri, 21 Aug 92 23:34:37 +0200 From: Magne.Haveraaen@ii.uib.no (Magne Haveraaen) Can anyone help me with accessible (in both senses of the word) references to algebraic (as in many-sorted algebraic specifications) or category theoretic definitions of linear algebra (real numbers, vector space, Banach space, Hilbert space, tensors, manifolds, etc.). Most books on linear algebra do this to some extent, but, after establishing the isomorphism between matrices and homomorphisms over vector spaces, the rest of the exposition is done in terms of the matrix representation. This is especially true for the area of tensors, which has developed its own peculiar notation. Magne Magne Haveraaen e-mail: magne@ii.uib.no Dept. of Informatics phone: +47 (5) 544154 University of Bergen fax: +47 (5) 544199 Hoyteknologisenteret N-5020 BERGEN Norway ============================================================================== Subj: Yoneda Date: 19 Aug 92 13:11:03 EST From: ------------- While we are asking terminological questions prompted by Mac Lane and Moerdijk, I'd like to know exactly what people mean by the Yoneda lemma. Does Yoneda include the fact that every presheaf is a canonical limit of representables? Does it include (as Johnstone has it, on _Topos Theory_ p.51) the claim that the Yoneda embedding to a presheaf category is left adjoint to the forgetful functor (i.e. the functor that forgets the action of arrows and only remembers the family of sets indexed over the objects of the domain category)? Colin McLarty ============================================================================== Subj: The square brackets notation for denotation Date: 26 Aug 92 08:42:15 EDT From: Charles Wells Topos theorists and people in denotational semantics use the notation [[t]] to denote a mathematical object that is the meaning of t in some semantics. In particular, in the case of a formula f, [[f]] is the truth value. APL and Donald Knuth use [f] for the truth value of a formula (or so I have been told). Does anyone know who used the double square bracket notation first (topos theorists, denotational semantics people, or whoever), and whether it was suggested by the APL usage? -- Charles Wells Department of Mathematics, Case Western Reserve University University Circle, Cleveland, OH 44106-7058, USA 216 368 2893 ============================================================================== Subj: 4 colours Date: Tue, 25 Aug 92 15:18:46 EDT From: pavlovic@triples.Math.McGill.CA (Dusko Pavlovic) A note describing A CATEGORICAL SETTING FOR THE 4-COLOUR THEOREM by Dusko Pavlovic is available by anonymous ftp. Abstract: It is well known that the 4-colouring of maps is equivalent to the 3-colouring of the edges of some graphs. We show that every slice of the category of 3-coloured graphs is a topos. The forgetful functor to the category of graphs is cotripleable; every loop-free graph is covered by a 3-coloured one in a universal way. In this context, the 4-Color Theorem becomes a statement about the existence of coalgebra structure on graphs. The "projective" approach to graphs, described here, is, in a sense, dual to the usual combinatorial treatment, based on induction. I shall try to relate the two approaches in another paper. How to get a copy: >ftp triples.math.mcgill.ca >login: anonymous >password:[your e-mail address] >cd pub/pavlovic >bin >get 4color-US.ps.Z %if your printer has American standards %or >get 4color-A4.ps.Z %otherwise >bye >uncompress 4color-++.ps.Z If you have any problems printing out this PS-file, please let me know. (I am not distributing the DVI or LaTeX versions of the paper because it contains several PS-diagrams.) Regards, Dusko ============================================================================== Subj: Re: Yoneda Date: Mon, 31 Aug 92 10:28:52 EDT From: pjf@saul.cis.upenn.edu (Peter Freyd) In the phrase "Yoneda lemma" the first word is generic. The connection with Yoneda is as follows. I wrote a letter to David Buchsbaum in 1959 in which I used one of the lemmas now known as Yoneda's. (I had seen the lemma in an abstract in the Notices by Watts.) Barry Mitchell, in a return letter, mentioned that the lemma was Yoneda's. In the book Abelian Categories I give a reference to a paper by Yoneda for the lemma. Some years after the publication of the book a student complained to me that the lemma does not appear in the cited paper. The complaint was duly passed on to Barry. He refered to his notes from the lectures that Mac Lane had given in the summer of 58 or 59 (I think) on Yoneda's treatment of the Ext functors, in which notes the lemma does appear. Barry had assumed that the lemma was in the paper that Saunders was reporting on. And, of course, I never thought of actually looking at a paper I was citing. But Yoneda must have known the Yoneda lemma. One may describe the Yoneda lemma as case zero of his theorems on Ext. The lemma certainly needs a name and Yoneda sounds nice. In that original formulation it is just the lemma that the maps from a functor represented by an object, A, to an arbitrary set-valued functor, F, are in natural corespondence with the elements of F(A). (Well, not quite: the original formulation was for additive categories and instead of "set-valued" it was "group-valued".) Almost immediately the phrase was generalized. I remember John Gray in the early 60's talking about the importance of the Yoneda lemma in enriched category settings. I don't know what Yoneda has to say about all of this. If he had stayed in pure mathematics he probably would have proved too many things to make the name useful as the sole description of a single lemma. As it is, though, the name serves well. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Mon, 31 Aug 92 11:10:01 EDT From: barr@triples.Math.McGill.CA (Michael Barr) As far as I am concerned the Yoneda is either the statement that NT(Hom(A,-),F) iso FA (naturally in A and F) of else the special case when F is also representable. The latter is probably the way Yoneda stated it. The rest is the Grothendieck construction or something. Michael ============================================================================== Subj: Re: Yoneda Date: Mon, 31 Aug 92 14:17:08 EDT From: barr@triples.Math.McGill.CA (Michael Barr) Peter's comments on the Yoneda lemma are interesting. Phil Scott was in Japan some years ago and actually spoke to Yoneda and it would be interesting to hear what he has to say. Computer scientists are fascinated by the fact that I actually know Kleisli and that he is still around. And that he actually did do the Kleisli construction. Michael ============================================================================== Subj: Re: square brackets Date: Mon, 31 Aug 92 09:34:02 +0100 From: Mike Fourman > From: Charles Wells > Topos theorists and people in denotational semantics use the > notation [[t]] to denote a mathematical object that is the > meaning of t in some semantics. In particular, in the case of a > formula f, [[f]] is the truth value. APL and Donald Knuth use [f] > for the truth value of a formula (or so I have been told). Does > anyone know who used the double square bracket notation first > (topos theorists, denotational semantics people, or whoever), > and whether it was suggested by the APL usage? The first occurrence I know of is in the Scott-Solovay treatment of Boolean-Valued models. I've always called them "Scott-open and Scott-close". Mike Prof. Michael P. Fourman email mikef@dcs.ed.ac.uk Dept. of Computer Science 'PHONE (+44) (0)31-650 5198 (sec) JCMB, King's Buildings, Mayfield Road, (+44) (0)31-650 5197 Edinburgh EH9 3JZ, Scotland, UK FAX (+44) (0)31 667 7209 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Mon, 31 Aug 92 09:34:24 BST From: Robert Tennent My guess is that logicians used it long before any of these did, and that the origin is that it evolved from parenthesized Quine corners: _ _ (| syntax |) Bob Tennent +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Mon, 31 Aug 1992 14:48:23 +0200 From: F.J.de.Vries@cwi.nl At least in 1975 Scott, Strachey and Stoy used such [[..]] notation, but it should be possible to go beyond that, as you do yourself perhaps with the reference to Knuth and APL. The question intrigued me because my reflex was to believe that the notiation should come from good old model theory. But that seems not be the case. Fer-Jan de Vries, CWI, Amsterdam. ++++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Mon, 31 Aug 92 10:23:03 EDT From: pavlovic@triples.Math.McGill.CA (Dusko Pavlovic) Some people call the double square brackets SCOTT BRACKETS. Could it be that Dana Scott first used them in 1967, in his notes on Boolean-valued models of set theory? Dusko Pavlovic +++++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Mon, 31 Aug 92 14:26:27 ADT From: dbenson@yoda.eecs.wsu.edu (David B. Benson) The first place I encountered this notation is Joseph E. Stoy Denotational Semanatics: The Scott-Strachey Approach to Programming Langauge theory The MIT Press, 1977 I quote from page 29: The brackets [[ ]], used round an argument of a semantic function, always enclose expressions in the object langauge, possibly including metalanguage variables. There appears to be no discussion of the history, other than Stoy perfers this to Quine's quasi-quotes (Quine's corners) Unfortunately, this book is, I believe, out-of-print. Regards to all, David ============================================================================== Subj: Yoneda and square brackets Date: Mon, 31 Aug 92 16:45:01 EDT From: es@math.mcgill.ca (Elaine Swan) To the best of my knowledge, the observation that every presheaf is a canonical limit of representables first appeared in ``Completions of categories'', Springer LNM 24 (1966). The double square brackets are usually associated with Dana Scott, Jim Lambek ============================================================================== Subject: Online LICS bibliography From: dmjones@theory.lcs.mit.edu (David M. Jones) Date: Mon, 31 Aug 92 16:52:54 EDT The online bibliography for the Annual IEEE Symposium on Logic in Computer Science has now been updated to include all of the papers published in the proceedings of the Seventh meeting, which took place in June 1992. The bibliography contains abstracts for all of the papers from the 1992 meeting. The bibliography, which is in BibTeX format, is available via anonymous ftp and mail server from theory.lcs.mit.edu [18.52.0.92] in the file pub/meyer/lics.bib. To retrieve the file via ftp, connect to theory using "anonymous" as the login name and "guest" as the password. To retrieve the file via mail server, send a message to the address archive-server@theory.lcs.mit.edu with the following line in the body: send meyer lics.bib An index of other available files can be retrieved with the command send meyer Index More information on the archive-server can be obtained by sending a message with only the word "help" in the body. David M. Jones MIT Lab for Computer Science Administrator, {types,logic,concurrency}@theory.lcs.mit.edu