From cat-dist Thu Jul 2 21:12:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA22806 for categories-list; Thu, 2 Jul 1998 20:21:43 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from aragorn.ics.muni.cz (aragorn.ics.muni.cz [147.251.4.33]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id KAA29439 for ; Thu, 2 Jul 1998 10:48:57 -0300 (ADT) X-Received: from queen.math.muni.cz (queen.math.muni.cz [147.251.80.1]) by aragorn.ics.muni.cz (8.8.5/8.8.5) with SMTP id PAA17922 for ; Thu, 2 Jul 1998 15:48:22 +0200 (MET DST) X-Received: by queen.math.muni.cz id AA06914 (5.67a8/IDA-1.4.4 for cat-dist@mta.ca); Thu, 2 Jul 1998 15:39:52 +0200 From: Jiri Rosicky Message-Id: <199807021339.AA06914@queen.math.muni.cz> Subject: categories: PSSL 68 To: cat-dist@mta.ca Date: Thu, 2 Jul 1998 15:39:52 +0200 (MET DST) X-Mailer: ELM [version 2.4ME+ PL25 (25)] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: ********* Second Announcement ********* The 68th Peripatetic Seminar on Sheaves and Logic August 29-30, 1998 Brno, Czech Republic The 68th meeting of the PSSL will be held at the Masaryk University, Brno, Czech Republic over the weekend of 29-30 August 1998. It is organized in connection with the federated conferences MFCS (Mathematical Foundations of Computer Science) and CSL (Computer Science Logic) which are taking place in Brno during August 23-28, 1998. There are other workshops related to MFCS\CSL and participants interested to stay in Brno the whole week may contact Jan Staudek (staudek@fi.muni.cz). As usual, the 68th meeting of the PSSL will be informal in nature and it will be focused on category theory, logic and theoretical computer science. We have arranged an accommodation in a student dormitory (single rooms, for 2 nights since Friday to Sunday) together with breakfasts and lunches in a university restaurant. The cost is 80$. Participants wishing to stay in hotels should contact Jan Staudek. Brno is located about 200 km south-east of Prague and 130 km north of Vienna and it can be reached from the both airports by trains and buses. More details will be available in the last announcement. We will maintain a www-page containing all informations. To register, please fill out the form below and return it (preferably by e-mail) to Jan Paseka till August 12. This deadline is important as afterwards we cannot guarantee an accommodation. Looking forward to meeting you in Brno. Jiri Rosicky and Jan Paseka Postal address: Jan Paseka Department of Mathematics Masaryk University Janackovo nam. 2a 66295 Brno Czech Republic email: paseka@math.muni.cz www: http://www.math.muni.cz/ftp/ftp/pub/math/people/Paseka/pssl68/pssl68.html _________________________________________________________________ 68th PSSL/MFCS Registration Form (e-mail) ----------------------------------------- I want to attend the 68th PSSL in Brno Name: Address: email: I wish to give a talk entitled: I wish to have the PSSL accommodation and meals: Special dietary requirements: __________________ Method of payment (all payment in US dollars): ---------------------------------------------- [] VISA [] MASTERCARD [] EUROCARD Please note that the amount your card will be charged depends on the actual change rate. Please make signed this Registration Form and send it to Jan Paseka. Amount to be payed: ________________ Cardholder's name: ---------------- Card no.: _________________ Exp: __/__/__ Sign:_____________________ [] Bank Checque / Eurochecque Please make check payable in US dollars to "Faculty of Informatics, Masaryk University" enclosed to signed this Registration Form and send all to Jan Paseka. Sign:_____________________ [] Bank transfer to Komercni banka, a.s. pobocka Brno-mesto nam. Svobody 21 631 31 Brno, Czech Republic SWIFT Code: KOMBCZPP Account Number: 85636621/0100 Account Number: 1234567890-1234567890 Details of Payment (Mandatory): 3375000498, < name > Be sure to clearly state 3375000498 and your name in Details of Payment. Amount of Payment : $ __________ Amount of Payment : __________ Kc For Czech participants (in accordance with current currency rate) Expected Date of Payment : ------------ _______________________________________________________________ From cat-dist Thu Jul 2 21:13:08 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA19287 for categories-list; Thu, 2 Jul 1998 20:22:15 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: rags owned process doing -bs Date: Thu, 2 Jul 1998 14:42:02 -0400 (EDT) From: "R.A.G. Seely" To: Categories List Subject: categories: Barrfest proceedings Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I have just (and finally!) sent off to Elsevier the package of papers to appear in the special issue of JPAA in honour of Mike Barr's 60th birthday. Readers of this list may be interested in the final "table of contents" - note that this volume still has to go through Elsevier's editorial process, so it may be a little while yet before we see the finished product on the shelf. - Robert Seely ----------------------------------------------------------------------- BarrFest Contents The Barrfest: A special issue of JPAA in honour of Mike Barr's 60th birthday The following papers will appear in the Barrfest issue of the Journal of Pure and Applied Algebra * Abramsky, Blute, & Panangaden: Nuclear and traced ideals in tensored *-categories * Banaschewski: A uniform view of localic realcompactness * Bunge & Funk: On a bicomma object condition for KZ-doctrines * Cegarra & Fernandez: Cohomology of cofibred categorical groups * Cockett & Seely: Linearly distributive functors * Gerstenhaber: Developments from Barr's thesis * Gran: Internal categories in Mal'cev categories * Janelidze & Tholen: Extended Galois theory and dissonant morphisms * Kennison: Synthetic solution manifolds for differential equations * Kinoshita, Power & Takeyama: Sketches * Lambek: Diagram chasing in ordered categories with involution * Mac Lane: The origins of mathematical abstraction * Mauri & Tierney: 2-descent, 2-torsors, and local equivalence * Moerdijk & Vermeulen: Proof of a conjecture of A. Pitts * Pedicchio & Wood: Groupoidal completely distributive lattices * Piessens & Steegmans: A decision procedure for semantical equivalence of thin FM specification * Shnider & van Osdol: Operads as abstract algebras, and the Koszul property * Sun: Remarks on Tannaka recovery of coalgebras >From the Introduction: "Mike's broad influence is reflected in this volume by the great breadth of materials which Mike inspired his friends to produce in his honour." The Editors: F.W. Lawvere, R.A.G. Seely ----------------------- From cat-dist Fri Jul 3 14:10:47 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA16162 for categories-list; Fri, 3 Jul 1998 13:18:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 3 Jul 1998 12:39:19 +0100 (BST) From: Paul Taylor Message-Id: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: co- Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: What are the origins of the co- prefix, as in coproduct, coequaliser ..., and who established their use? Has anybody ever thought through and written down any guidelines on which of a pair of dual concepts is co-? Who is reponsible for dropping this prefix from cofinal? (A mistake, IMHO). Paul From cat-dist Fri Jul 3 14:12:18 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA25248 for categories-list; Fri, 3 Jul 1998 13:18:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 2 Jul 1998 22:10:56 -0400 (EDT) From: Susan Niefield To: categories@mta.ca Subject: categories: withdrawal of preprint In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The paper "Exponentiablity and Single Universes" by Marta Bunge and Susan Niefield, recently announced on the site ww1.union.edu/~niefiels has been temporarily withdrawn. A revised version will be posted soon. The paper contained an erroneous result - namely, that for an arbitrary small category B, the category UFL/B of Giraud-Conduche fibrations over B is a topos. A counterexample has been found by Peter Johnstone. From cat-dist Fri Jul 3 15:08:05 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA20677 for categories-list; Fri, 3 Jul 1998 14:17:31 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 3 Jul 1998 13:09:52 -0400 (EDT) From: James Stasheff To: Paul Taylor cc: categories@mta.ca Subject: categories: Re: co- In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Surely it goes back at least to cohomology or further to covariant and contravariant with their contravariant meanings ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 On Fri, 3 Jul 1998, Paul Taylor wrote: > What are the origins of the co- prefix, as in coproduct, coequaliser ..., > and who established their use? > > Has anybody ever thought through and written down any guidelines on > which of a pair of dual concepts is co-? > > Who is reponsible for dropping this prefix from cofinal? > (A mistake, IMHO). > > Paul > From cat-dist Sat Jul 4 10:35:37 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA14259 for categories-list; Sat, 4 Jul 1998 09:54:29 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 3 Jul 1998 15:44:49 -0400 (EDT) From: John R Isbell Reply-To: John R Isbell To: Paul Taylor cc: categories@mta.ca Subject: categories: re: co-: P.S. Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: In the last sentence of my Re: categories: co-, insert 'from "cofinal"'. From cat-dist Sat Jul 4 10:35:48 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA16463 for categories-list; Sat, 4 Jul 1998 09:48:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 3 Jul 1998 15:37:48 -0400 (EDT) From: John R Isbell To: Paul Taylor cc: categories@mta.ca Subject: categories: Re: co- In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: On Fri, 3 Jul 1998, Paul Taylor wrote: > What are the origins of the co- prefix, as in coproduct, coequaliser ..., > and who established their use? > > Has anybody ever thought through and written down any guidelines on > which of a pair of dual concepts is co-? > > Who is reponsible for dropping this prefix from cofinal? > (A mistake, IMHO). > > Paul > Fragments: (1) Origin, I don't know, but surely cohomology is where it started. The term was used very early, 1937 I think, by Norman Steenrod in a paper mainly on universal coefficient theorems. (2) The idea of putting forward some such guidelines was seriously discussed at La Jolla 1965, and I should say that Sammy Eilenberg killed it single-handed. His main point was that anything we Americans might propose would be absolutely unacceptable in Paris. Verdier was the only Frenchman present; he was well thought of but very young. (1 bis) Of course not covariant-contravariant. (3) I'm not sure what "A mistake IMHO" means. Of course, the "co" in cofinal is genetically "con" of congress, concatenation. I don't have nice illustrations of antecedents of co-homology but it is not 'together' like in congress & concatenation. But it is dropped in categorical contexts because it is a distracting "co". John Isbell From cat-dist Sat Jul 4 10:35:49 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA04968 for categories-list; Sat, 4 Jul 1998 09:53:12 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: graham@pophost.dcs.qmw.ac.uk Message-Id: In-Reply-To: References: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 3 Jul 1998 20:40:02 +0100 To: categories@mta.ca From: Graham White Subject: categories: Re: co- Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: >Surely it goes back at least to cohomology >or further to covariant and contravariant >with their contravariant meanings > >************************************************************ > Until August 10, 1998, I am on leave from UNC > and am at the University of Pennsylvania > > Jim Stasheff jds@math.upenn.edu > > 146 Woodland Dr > Lansdale PA 19446 (215)822-6707 > > > > Jim Stasheff jds@math.unc.edu > Math-UNC (919)-962-9607 > Chapel Hill NC FAX:(919)-962-2568 > 27599-3250 > > >On Fri, 3 Jul 1998, Paul Taylor wrote: > >> What are the origins of the co- prefix, as in coproduct, coequaliser >>..., >> and who established their use? >> >> Has anybody ever thought through and written down any guidelines on >> which of a pair of dual concepts is co-? >> >> Who is reponsible for dropping this prefix from cofinal? >> (A mistake, IMHO). >> >> Paul >> I would have thought that `co' in `cofinal' means `together with', and didn't originally mean `opposite'. There are instances of this meaning of `co' in, for example, `coroutine'. And, of course, `covariant', which is well established in 19th century invariant theory, where it contrasts with `invariant' (but I can't remember offhand a 19th cent. use of `contravariant'). It would be very interesting to see a history of this terminology. Graham From cat-dist Sat Jul 4 10:38:07 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA15691 for categories-list; Sat, 4 Jul 1998 09:50:24 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 3 Jul 1998 15:28:57 -0400 (EDT) From: Michael Barr To: Paul Taylor cc: categories@mta.ca Subject: Re: categories: co- In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Well, I am speculating here. But FWIW, here goes. Back in prehistory, there were covariant and contravariant tensors. Later on, came homology, a word with impeccable credentials. The dual was called cohomology, the co- doubltess a shortening of contra-. Very bad choice. But that's the way it came. Peter Hilton pointed out that "homology" should be generic with cohomology as the covariant version and contrahomology as the contravariant one. I think he wrote a book using "homology" and "contrahomology", a kind of intermediate step. Good idea, but hopeless, really. It reminds me of my pet peeve, which is the use of the horseshoe for included-in-or-equal. Thus destroying the analogy with <, as well as requiring the idiotic horseshoe-plus-not-equal, which does not even appear in the standard fonts. So I never use the plain horseshoe for anything. If everybody did that, then after one generation mathematicians could start using the horseshoe for proper inclusion. It will never happen. As for which is which, that is a harder question. If D is a diagram, cone(-,D) is contravariant, but a representing object is called a limit of D. But limit is covariant in D. The opposite is true of cocones and colimits. Which one is right? Hard to say? I call a reflective subcategory one whose inclusion has a left adjoint, but that has been called coreflective (although probably not in recent years). The co- in cofinal has nothing to do (except perhaps very indirectly) with the one in colimit. I think it is like the co- in coordinate. As such, I see nothing wrong with final. Or rather, I don't see that cofinal is any improvement. A family of objects in a category is weakly final (or weakly terminal) if every object in the category has at least one arrow to at least one object of said family. Replace both "at least"s by "exactly" and you have a final (or terminal) family and require the family to be singleton and you have a final (or terminal) object. So final ought to be weakly final and similarly for cofinal, but I don't expect anyone's usage will change. From cat-dist Sat Jul 4 14:51:20 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA25578 for categories-list; Sat, 4 Jul 1998 14:15:39 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Peter Selinger Message-Id: <199807041502.RAA06215@harald.daimi.aau.dk> Subject: categories: Re: co- To: pt@dcs.qmw.ac.uk (Paul Taylor) Date: Sat, 4 Jul 1998 17:02:15 +0200 (MET DST) Cc: categories@mta.ca In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> from Paul Taylor at "Jul 3, 98 12:39:19 pm" X-Mailer: ELM [version 2.4ME+ PL22 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I would guess that the oldest use of co- in mathematics is to mean "complement of an angle", as in cosine, cotangent, etc. Encyclopedia Britannica dates these to 1635. This would be an early justification of using co- in the sense of "opposite". The word "complement" itself comes from Latin "complere": to fill up. The use of co- in the sense of "together, joint" is much more widespread in everyday language, in words such as coauthor and coconspirator (notice how the last example is curiously redundant). This is also the origin of words such as coordinate (1641), coefficient (ca. 1715), and collinearity (1863). Best wishes, -- Peter (Source: Encyclopedia Britannica) > From Paul Taylor: > What are the origins of the co- prefix, as in coproduct, coequaliser ..., > and who established their use? > > Has anybody ever thought through and written down any guidelines on > which of a pair of dual concepts is co-? > > Who is reponsible for dropping this prefix from cofinal? > (A mistake, IMHO). > > Paul From cat-dist Sat Jul 4 14:51:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA19162 for categories-list; Sat, 4 Jul 1998 14:14:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 4 Jul 1998 10:07:02 -0400 (EDT) From: James Stasheff To: John R Isbell cc: Paul Taylor , categories@mta.ca Subject: categories: Re: co- In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I do not understand (1 bis) Of course not covariant-contravariant. Surely that is what Steenrod had in mind (subconsciously)? Remember that covariant-contravariant for diff forms wass originally referring to change of coordiates rather than maps. ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 On Fri, 3 Jul 1998, John R Isbell wrote: > > On Fri, 3 Jul 1998, Paul Taylor wrote: > > > What are the origins of the co- prefix, as in coproduct, coequaliser ..., > > and who established their use? > > > > Has anybody ever thought through and written down any guidelines on > > which of a pair of dual concepts is co-? > > > > Who is reponsible for dropping this prefix from cofinal? > > (A mistake, IMHO). > > > > Paul > > > Fragments: (1) Origin, I don't know, but surely cohomology > is where it started. The term was used very early, 1937 I think, > by Norman Steenrod in a paper mainly on universal coefficient > theorems. > (2) The idea of putting forward some such > guidelines was seriously discussed at La Jolla 1965, and I > should say that Sammy Eilenberg killed it single-handed. His > main point was that anything we Americans might propose would > be absolutely unacceptable in Paris. Verdier was the only > Frenchman present; he was well thought of but very young. > (1 bis) Of course not covariant-contravariant. > (3) I'm not sure what "A mistake IMHO" means. > Of course, the "co" in cofinal is genetically "con" of > congress, concatenation. I don't have nice illustrations of > antecedents of co-homology but it is not 'together' like in > congress & concatenation. But it is dropped in categorical > contexts because it is a distracting "co". > John Isbell > > From cat-dist Sat Jul 4 14:52:35 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA19818 for categories-list; Sat, 4 Jul 1998 14:16:35 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 4 Jul 1998 11:36:35 -0400 (EDT) From: John R Isbell To: Paul Taylor cc: categories@mta.ca Subject: categories: Re: co- Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The Shorter OED is doubtless not an infallible guide to mathematical etymology, but it has something obvious that we have all been missing (as far as I have seen yet): <2 {\it Math.} Short for {\it complement}, in the sense 'of the complement' (as {\it cosine}), or 'complement of' (as {\it co-latitude}).> All categorical 'co's are surely that kind. In prticular, cohomology like cosine. If Steenrod had in mind covariant, contravariant, why would he say 'cohomology'? Had he said 'contrahomology' it would be clear. (It is relevant, I think, that in Lefschetz' first Colloquium book he called cohomology, such as $H^1$, homology in negative dimensions, as $H_{-1}$.) Cofinal has to be Latin 'cum'+final. John From cat-dist Sat Jul 4 14:53:36 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA19255 for categories-list; Sat, 4 Jul 1998 14:15:12 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 4 Jul 1998 10:09:29 -0400 (EDT) From: James Stasheff To: Michael Barr cc: Paul Taylor , categories@mta.ca Subject: categories: Re: co- In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: OK what is the origin/meaning of co in coordinate perhaps it's time to treat this LESS seriously as int hold canard cobras are bras with the eros reversed ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Sat Jul 4 15:12:23 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA19826 for categories-list; Sat, 4 Jul 1998 14:35:07 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: co- To: categories@mta.ca Date: Sat, 4 Jul 1998 18:30:40 +0100 (BST) X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: From: "Dr. P.T. Johnstone" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Of course the "co-" in "cofinal" is the Latin "cum", as it normally is in English (if I refer to someone as my co-conspirator, I mean he is conspiring with me, not against me!). But category-theorists have got so firmly into the habit of using "co-" as an abbreviation for "contra-" (except in the terms covariant and contravariant -- I assume they survived because they were widely used before categories came along) that the "co-" in "cofinal" had to go. As for who killed it off, the evidence points to Saunders Mac Lane as the guilty party (see p. 213 of Categories for the Working Mathematician). Category-theorists at least have the defence that the algebraic topologists had started using "cohomology" for what should have been "contrahomology" before categories came along. As Mike Barr mentioned, Hilton and Wylie tried to encourage the use of "contrahomology" in their book (1960), but it was probably far too late by then. I'm surprised that no-one has yet mentioned Barry Mitchell's attempt, in his book, to "eliminate the words left and right" from the language of category theory. He did have a scheme for deciding which of a dual pair of concepts should have the "co-"; unfortunately it led him to use "adjoint" and "coadjoint" in the opposite sense to that in which most people had been using them, and so much confusion resulted that everyone went back to "left adjoint" and "right adjoint". If it were possible to start afresh with the terminology of category theory (of course it isn't, as Mike pointed out), I'd be in favour of using "left" and "right" as much as possible, and eliminating the "co-"s. (But even this is not guaranteed free from ambiguity. Has anyone apart from me (and, I suppose, the authors) noticed that the usage of the terms "left coset" and "right coset" in Mac Lane & Birkhoff's Algebra is the opposite of that in Birkhoff & Mac Lane?) Peter Johnstone From cat-dist Sat Jul 4 15:14:26 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA17209 for categories-list; Sat, 4 Jul 1998 14:35:56 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 4 Jul 1998 13:33:23 -0400 (EDT) From: John R Isbell To: Paul Taylor cc: categories@mta.ca Subject: categories: Re: co- In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Well, the cosine makes a really beautiful story. Negative-dimensional chains are not in Lefschetz' first Colloquium book, but his second. In 1942, so the co- terminology did not sweep all before it. In Lefschetz' first Colloquium book cocycles are . In Steenrod's universal coefficient theorems (1936, not 1937) cohomology is . Eilenberg-Steenrod 'Foundations' has a fairly extensive historical note at the end of Chapter 1. In particular, they credit 'co' to Whitney, Annals 39 (1938) 397-430 or so (397 is exact). Whitney has a very brief history on p. 398, tracing the concept to Alexander 1922, and mentioning a covariant tensor in Alexander 1935. He says nothing of why he likes co-. John From cat-dist Sun Jul 5 14:07:11 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA02394 for categories-list; Sun, 5 Jul 1998 12:51:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sun, 5 Jul 1998 07:52:45 -0400 (EDT) From: James Stasheff To: Peter Selinger cc: Paul Taylor , categories@mta.ca Subject: categories: Re: co- In-Reply-To: <199807041502.RAA06215@harald.daimi.aau.dk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: >This is also the origin of words such as coordinate (1641), coefficient (ca. 1715), and collinearity (1863). co-linear I see as together or joint but what is `ordinate' and what is `effcient'?? ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Sun Jul 5 14:07:15 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id MAA00006 for categories-list; Sun, 5 Jul 1998 12:50:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: co- To: categories@mta.ca Date: Sat, 4 Jul 1998 18:40:15 +0100 (BST) X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: From: "Dr. P.T. Johnstone" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: P.S. -- I don't agree with John that "all categorical 'co-'s" are of the same kind as "cosine" or "colatitude" in referring to something complementary (although I suppose that "cohomology" might be). I can't see any sense in which the opposite of a category can be regarded as complementary to it. Peter Johnstone From cat-dist Mon Jul 6 14:40:58 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA01968 for categories-list; Mon, 6 Jul 1998 13:39:36 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sun, 5 Jul 1998 13:12:25 -0400 (EDT) From: John R Isbell To: James Stasheff cc: Peter Selinger , Paul Taylor , categories@mta.ca Subject: Re: categories: Re: co- In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I can't fit this On Sun, 5 Jul 1998, James Stasheff wrote: > >This is also the origin of words such as coordinate (1641), > coefficient (ca. 1715), and collinearity (1863). > > co-linear I see as together or joint > but what is `ordinate' and what is `effcient'?? > remark to coefficients, but when I studied analytics in 1945, x was the abscissa and y the ordinate. Presumably z would be the coordinate. John From cat-dist Mon Jul 6 14:40:59 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA26387 for categories-list; Mon, 6 Jul 1998 13:40:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Peter Selinger Message-Id: <199807051811.UAA25902@harald.daimi.aau.dk> Subject: categories: Re: co- To: jds@math.upenn.edu (James Stasheff) Date: Sun, 5 Jul 1998 20:10:59 +0200 (MET DST) Cc: selinger@daimi.aau.dk, pt@dcs.qmw.ac.uk, categories@mta.ca In-Reply-To: from James Stasheff at "Jul 5, 98 07:52:45 am" X-Mailer: ELM [version 2.4ME+ PL22 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: > From James Stasheff: > >This is also the origin of words such as coordinate (1641), > coefficient (ca. 1715), and collinearity (1863). > > co-linear I see as together or joint > but what is `ordinate' and what is `effcient'?? I am certainly no linguist, but it seems obvious to me that in all three cases, the prefix was attached before the word entered the English language, and possibly even before the word acquired its mathematical meaning. Coordinate: from Latin ordinare: to arrange, to put in order. Coordinates are for "arranging" points in the plane, and they do this jointly. Compare: coordination. Coefficient: from Latin efficere: to affect, to produce an effect (?). Coefficients are parameters that affect some quantity, and usually there is more than one, so again, they do it jointly. Does anyone know the actual origin of the word "covariant"? My guess is that in the original context of tensors on manifolds, it is a contraction of "coordinate invariant", that is, invariant under transformations of coordinate systems. If this is true, then it fits neither the "jointly" nor the "complement" nor the "dual" schemes. Despite the fact that it came first historically, it would seem that the word "covariant" is an exception to the otherwise (more or less) consistent use of the prefix co- in category theory. If one were to change terminology to eliminate this oddity, it would make little sense to change the rule to accomodate the exception - rather, one should rename "covariant" to something more logical like "provariant". I doubt that it would be worth the effort -- especially since the word "covariant" only ever seems to appear in parentheses. Best, -- Peter From cat-dist Mon Jul 6 14:41:09 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA21019 for categories-list; Mon, 6 Jul 1998 13:44:10 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 6 Jul 1998 16:07:47 +0100 (BST) From: Ronnie Brown X-Sender: mas010@publix To: categories@mta.ca Subject: categories: co etc Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Re Hilton and Wylie: it really was a landmark in its time, quite readable. But the co- contra- change, together with contravariant functors written on the right, became contrafusing. Ronnie From cat-dist Mon Jul 6 14:42:06 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA04420 for categories-list; Mon, 6 Jul 1998 13:43:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807060648.QAA18685@zeus.mpce.mq.edu.au> X-Sender: mbatanin@zeus.mpce.mq.edu.au Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Mon, 6 Jul 1998 16:49:05 +1000 To: categories@mta.ca From: mbatanin@mpce.mq.edu.au (Michael Batanin) Subject: categories: generalized computads Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear collegues, the following preprint "Computads for finitary monads on globular sets" is available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html >From Introduction. This work arose as a reflection on the foundation of higher dimensional category theory. One of the main ingredients of any proposed definition of weak $n$-category is the shape of diagrams (pasting scheme) we accept to be composable. In a globular approach \cite{Bat} each $k$-cell has a source and target $(k-1)$-cell. In the opetopic approach of Baez and Dolan \cite{BD} and the multitopic approach of Hermida, Makkai and Power \cite{HMP} each $k$-cell has a unique $(k-1)$-cell as target and a whole $(k-1)$-dimensional pasting diagram as source. In the theory of strict $n$-categories both source and target may be a general pasting diagram \cite{J,StH, StP}. The globular approach being the simplest one seems too restrictive to describe the combinatorics of higher dimensional compositions. Yet, we argue that this is a false impression. Moreover, we prove that this approach is a basic one from which the other type of composable diagrams may be derived. One theorem proved here asserts that the category of algebras of a finitary monad on the category of $n$-globular sets is {\bf equivalent} to the category of algebras of an appropriate monad on the special category (of computads) constructed from the data of the original monad. In the case of the monad derived from the universal contractible operad \cite{Bat} this result may be interpreted as the equivalence of the definitions of weak $n$-categories (in the sense of \cite{Bat}) based on the `globular' and general pasting diagrams. It may be also considered as the first step toward the proof of equivalence of the different definitions of weak $n$-category. We also develop a general theory of computads and investigate some properties of the category of generalized computads. It turned out, that in a good situation this category is a topos (and even a presheaf topos under some not very restrictive conditions, the property firstly observed by S.Schanuel and reproved by A,Carboni and P.Johnstone for $2$-computads in the sense of Street). /\ / \ M --/ Co \--> MQ / A C T\ /________\ Centre of Australian Category Theory Mathematics Department, Macquarie University New South Wales 2109, AUSTRALIA From cat-dist Mon Jul 6 14:45:20 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA27126 for categories-list; Mon, 6 Jul 1998 13:43:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Real-To: Message-Id: <3.0.32.19980706091639.00e45b50@pop.apk.net> X-Sender: cwells@pop.apk.net X-Mailer: Windows Eudora Pro Version 3.0 (32) Date: Mon, 06 Jul 1998 09:16:48 -0400 To: categories@mta.ca From: Charles Wells Subject: categories: Left and right Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: >If it were possible to start afresh with the terminology of category >theory (of course it isn't, as Mike pointed out), I'd be in favour of >using "left" and "right" as much as possible, and eliminating the "co-"s. >(But even this is not guaranteed free from ambiguity. Has anyone apart >from me (and, I suppose, the authors) noticed that the usage of the >terms "left coset" and "right coset" in Mac Lane & Birkhoff's Algebra >is the opposite of that in Birkhoff & Mac Lane?) Not all lefts and rights are the same. Left adjoint refers to the fact that arrows FROM a value of the left adjoint into an object correspond to arrows INTO the value of the right adjoint at that object. Since English is written left to right, Hom(A,B) means arrows from A to B, so in the equation Hom(FA, B) = Hom(A,UB) the F winds up on the left side of the hom set. This is a natural name given the way we write our language, and so it is not hard to reconstruct what the phrases left and right adjoint mean. On the other hand the left and right in "left inverse" and "right inverse" depend on the order in which we write composition, and that is independent of the way we write our language. I for one can never remember which is which, a learning disability no doubt accounted for by the fact that I worked on semigroups before I became a category theorist, leaving me without a default way to write composition. In any case, I would like names such as retraction and split. Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html From cat-dist Mon Jul 6 14:48:01 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA30319 for categories-list; Mon, 6 Jul 1998 13:40:47 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: duskin@buffnet.net Message-Id: In-Reply-To: References: <199807041502.RAA06215@harald.daimi.aau.dk> Mime-Version: 1.0 Content-Type: text/enriched; charset="us-ascii" Date: Sun, 5 Jul 1998 17:24:31 -0400 To: categories@mta.ca From: John Duskin Subject: categories: Re: co- Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I seem to remember the "ordinate" (=y) and "abscissa" (=x) as making up the cartesian "co-ordinates " of the point (x,y). "co-efficient" probably comes from terminology for polynomials, with the "co-" coming from the fact that it was always atttached to a power of x. And while we are on this we shouldn't forget "direct" and "inverse" and "inductive" and "projective" limits! It took category theory (and Mac Lane) to make sense of all of this. From cat-dist Mon Jul 6 14:53:40 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA05446 for categories-list; Mon, 6 Jul 1998 13:45:43 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Mon, 6 Jul 1998 12:02:12 -0400 (EDT) From: Michael Barr To: "Dr. P.T. Johnstone" cc: categories@mta.ca Subject: categories: Re: co- In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Well, after reading the various replies, I concede that I was very likely wrong about cohomolohy (which is generally accepted as the first co-) being short for contra-homology. Therefore, complementary homology seems the best. Then people started thinking of it as covariant homology anyway. Then the idea took hold that co-meant opposite. Strange, since now it has essentially reversed meaning. That's how the language developes. It is through such twists and turns that the same Indo-european root come to mean black in English and white in French (and other romance languages). A few other comments. The x- and y-coordinates are (or used to be) called ordinate and abscissa (or vice versa). For what it's worth. I know what efficient means, but I have no idea what it has to do with coefficient. It stands to reason that Birkhoff & Mac Lane is the opposite of Mac Lane & Birkhoff. I hadn't noticed that, but I sure had noticed that I had no simple way of recalling which were left and which were right cosets. And would products be left limits or right limits and why? Michael On Sat, 4 Jul 1998, Dr. P.T. Johnstone wrote: > P.S. -- I don't agree with John that "all categorical 'co-'s" > are of the same kind as "cosine" or "colatitude" in referring to > something complementary (although I suppose that "cohomology" > might be). I can't see any sense in which the opposite of a > category can be regarded as complementary to it. > > Peter Johnstone > From cat-dist Mon Jul 6 17:17:36 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA04585 for categories-list; Mon, 6 Jul 1998 16:03:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 6 Jul 1998 19:15:35 +0100 (BST) From: Paul Taylor Message-Id: <199807061815.TAA19455@ruby.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: co- Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I seem to have started an avalanche. There seem to be two contradictory theories - maybe someone could make the codictory. 1. co- versus nothing, from trigonometry 2. co- versus contra- I knew the words covariant and contravariant both before I knew anything about categories, and from a book which predated (sorry, pre-dated) category theory, namely A.S. Eddington's "Mathematical Theory of Relativity" (1925), which was the only serious maths book I could find in the town library in High Wycombe (half way between London and Oxford) when I was at school. What it was doing there, I can't imagine. As to "cofinal", I worked out its etymology for myself, but Saunders Mac Lane (if he was in fact the culprit) could have re-invented its etymology instead of generating the confusion. Besides, (co)final functors are those between diagram-shapes which give rise to the same colimits, so the prefix seems reasonable to me. Paul From cat-dist Tue Jul 7 11:17:03 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA04031 for categories-list; Tue, 7 Jul 1998 09:10:43 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807062150.OAA08141@coraki.Stanford.EDU> To: categories@mta.ca Subject: categories: A sense in which C^op is complementary to C In-reply-to: Your message of "Sat, 04 Jul 1998 18:40:15 +0100." Date: Mon, 06 Jul 1998 14:50:29 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: From: "Dr. P.T. Johnstone" >I can't see any sense in which the opposite of a >category can be regarded as complementary to it. Peter's book "Stone spaces" (CUP 1982) studies many categories that obey the rule that the signature of the opposite of C is the complement of the signature of C, with respect to both existence and direction of sup's and inf's of cardinalities 0, finite nonzero, and infinite. Namely, if sup's of a given arity exist in C then inf's of that arity do not exist in C^op, and conversely (at least in the examples). The extremal pair of opposite categories in this regard are CABA, complete atomic Boolean algebras, which has all inf's and sup's, dual to Set having none (but for this purpose we could as well take StoneDLat, dual to Poset). "In the middle" is CSLat, complete semilattices, having sup's of all cardinalities and no inf's, dual to itself via a duality that interchanges sup's and inf's (not to be confused with the equivalence that performs this interchange). Top and bottom as zeroary sup and inf can be moved independently from CABA to Set to give pointed and bipointed sets dual to CABA's lacking one or both constants 0 and 1. Likewise binary (and hence ternary etc.) sup and/or inf can be moved from CABA to Set. Moving all finitary sup's for example turns Set into SLat (semilattices, specifically of the meet kind) and CABA into StoneSLat, aka algebraic lattices. By viewing Stone topology as the manifestation of infinite sup's and inf's, the duality of Stone (Stone spaces) and Bool (Boolean algebras) can be understood as the migration of the infinitary sup's and inf's of CABA to Set, turning CABA into Bool and Set into Stone. From this viewpoint the ability to present limits in Top follows by duality from the optional removal in CABA of infinitary inf's to yield Top^op, while Frm (frames) as Loc^op (locales) tightens this up by removing "optional". Chu(Set,2) provides a uniform setting for this rule. All the above categories C have a "common" full concrete embedding in Chu(Set,2) in which the points remain unchanged (concreteness) while the states or opens are taken to be the morphisms of C to the realization of the schizophrenic object 2 as an object of C. In this setting the above tendency (but not the converse part) can be made a theorem about Chu spaces over 2 as follows, at least for the finitary operations. Theorem 0: If a space A has constant 0 then its dual A\perp does not have constant 1 (and dually with 0 and 1 interchanged). Proof. A row of all 0's precludes a column of all 1's (the impossibility of having an irresistible force and an immovable object). Theorem 2: If A has all binary joins then the only binary meets existing in A\perp are of comparable elements. Proof. Suppose x,y are incomparable columns of A (points of A\perp) whose meet x&y is a column of A. Then there exist rows a,b of A such that x y x&y a 0 1 0 b 1 0 0 is part of A's matrix. Now form the join of a and b: a|b 1 1 0 This contradicts x&y being the meet of x and y. QED (Apropos of the comparability issue, note that the category of finite chains with bottom, with morphisms all monotone bottom-preserving functions, is self-dual.) I don't know how to state the corresponding theorem if any for infinitary sup's and inf's. And I have no idea how to generalize all this to Chu(Set,3) and beyond. I became aware of this complementarity principle for opposite categories around 1990, and contemplating it led my student Vineet Gupta and myself to (ordinary) Chu spaces in 1992, at which point we learned that they were not new (but not well known). Vaughan Pratt From cat-dist Tue Jul 7 12:36:32 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA11151 for categories-list; Tue, 7 Jul 1998 11:09:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807070048.KAA19559@macadam.mpce.mq.edu.au> X-Sender: street@macadam.mpce.mq.edu.au Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 7 Jul 1998 10:49:43 +1000 To: categories@mta.ca From: street@mpce.mq.edu.au (Ross Street) Subject: categories: re: co- Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: While our insecurities about "co-" are being aired, I thought I should admit to even more worries in the case of 2-categories (or bicategories)! In these terminological matters, I have given up on linguistic correctness and have also almost given up worrying about mathematical consistency. Here is the difficulty. Motivation for 2-category theory comes from (at least) two different directions which often lead to the same basic concepts yet with different suggestions for terminology for the three other dual concepts. Each concept has a co-, op-, and coop-version but the good choice of op or co is not clear at all. First motivation: We can take the view that our 2-category is foremost a category with the 2-cells as extra structure (like homotopies in Top). Then, for example, as pointed out by John Gray in the La Jolla 1965 volume, Grothendieck was wrong in using "cofibration" for the *2-cell*-reversing dual of fibration. Compare the situation in Top where cofibrations are the *arrow*-reversing dual of fibrations. So this leads to "opfibration" for the *2-cell*-reversing dual of "fibration" (this is unnecessary in Top since homotopies are invertible). However, Grothendieck's terminology has stuck in some literature. Using this first motivation, we define products and coproducts of objects in a 2-category as we would in a category plus an extra 2-cell condition. Second motivation: We think of our 2-category K as a place to develop category theory so that arrows f : U --> A into an object A of K are thought of as generalised objects of A, and 2-cells into A are generalised arrows of A. Take a notion such as monad on A. From this motivation, reversing *2-cells* in K, we should get the notion of "comonad". This terminology is in conflict with the doctrine developed on the basis of the first motivation. Of course, "monad" is invariant under *arrow*-reversal, but there are other concepts which are not. --Ross From cat-dist Tue Jul 7 15:06:03 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA28350 for categories-list; Tue, 7 Jul 1998 13:48:46 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 7 Jul 1998 08:09:41 -0400 (EDT) From: James Stasheff To: Charles Wells cc: categories@mta.ca Subject: categories: Re: Left and right In-Reply-To: <3.0.32.19980706091639.00e45b50@pop.apk.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Not to mention the notation Ext(A,B) in which B is extended BY A ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 On Mon, 6 Jul 1998, Charles Wells wrote: > > >If it were possible to start afresh with the terminology of category > >theory (of course it isn't, as Mike pointed out), I'd be in favour of > >using "left" and "right" as much as possible, and eliminating the "co-"s. > >(But even this is not guaranteed free from ambiguity. Has anyone apart > >from me (and, I suppose, the authors) noticed that the usage of the > >terms "left coset" and "right coset" in Mac Lane & Birkhoff's Algebra > >is the opposite of that in Birkhoff & Mac Lane?) > > Not all lefts and rights are the same. Left adjoint refers to the fact > that arrows FROM a value of the left adjoint into an object correspond to > arrows INTO the value of the right adjoint at that object. Since English > is written left to right, Hom(A,B) means arrows from A to B, so in the > equation Hom(FA, B) = Hom(A,UB) the F winds up on the left side of the hom > set. This is a natural name given the way we write our language, and so it > is not hard to reconstruct what the phrases left and right adjoint mean. > > On the other hand the left and right in "left inverse" and "right inverse" > depend on the order in which we write composition, and that is independent > of the way we write our language. I for one can never remember which is > which, a learning disability no doubt accounted for by the fact that I > worked on semigroups before I became a category theorist, leaving me > without a default way to write composition. In any case, I would like > names such as retraction and split. > > > Charles Wells, Department of Mathematics, Case Western Reserve University, > 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. > EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. > FAX: 216 368 5163. HOME PHONE: 440 774 1926. > HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html > From cat-dist Tue Jul 7 15:06:52 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA28563 for categories-list; Tue, 7 Jul 1998 13:48:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 7 Jul 1998 08:07:35 -0400 (EDT) From: James Stasheff To: Ronnie Brown cc: categories@mta.ca Subject: categories: Re: co etc In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: inspite of the book being coproductive ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 On Mon, 6 Jul 1998, Ronnie Brown wrote: > > Re Hilton and Wylie: it really was a landmark in its time, quite readable. > But the co- contra- change, together with contravariant functors written > on the right, became contrafusing. > > Ronnie > > From cat-dist Tue Jul 7 21:00:10 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA09470 for categories-list; Tue, 7 Jul 1998 20:09:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <35A27691.CEAF45BC@iswest.com> Date: Tue, 07 Jul 1998 15:27:14 -0400 From: Zhaohua Luo X-Mailer: Mozilla 4.05 [en] (Win95; I) MIME-Version: 1.0 To: Vaughan Pratt CC: categories@mta.ca Subject: categories: Re: A sense in which C^op is complementary to C References: <199807062150.OAA08141@coraki.Stanford.EDU> Content-Type: multipart/alternative; boundary="------------9DA47DF35DB9657A80A57DB9" Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: --------------9DA47DF35DB9657A80A57DB9 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit A category is called " left " if it has a strict initial object and any map with an initial domain is regular (in the general sense). The opposite of a left category is called a " right " category. The key fact here is that a left category is never right unless it is trivial (i.e. any map is an isomorphism). Since may natural categories are either left or right, this enable us to introduce the "relative version" of a categorical concept with a dual. The following short note On Left and Right Categories is available at www.azd.com/lrcat.html which is inspired by Vaughan Pratt comments: Vaughan Pratt wrote: > From: "Dr. P.T. Johnstone" > >I can't see any sense in which the opposite of a > >category can be regarded as complementary to it. > > Peter's book "Stone spaces" (CUP 1982) studies many categories that > obey the rule that the signature of the opposite of C is the complement > of the signature of C, with respect to both existence and direction > of sup's and inf's of cardinalities 0, finite nonzero, and infinite. > Namely, if sup's of a given arity exist in C then inf's of that arity > do not exist in C^op, and conversely (at least in the examples). > > The extremal pair of opposite categories in this regard are CABA, > complete atomic Boolean algebras, which has all inf's and sup's, dual to > Set having none (but for this purpose we could as well take StoneDLat, > dual to Poset). "In the middle" is CSLat, complete semilattices, > having sup's of all cardinalities and no inf's, dual to itself via a > duality that interchanges sup's and inf's (not to be confused with the > equivalence that performs this interchange). > > Top and bottom as zeroary sup and inf can be moved independently from > CABA to Set to give pointed and bipointed sets dual to CABA's lacking > one or both constants 0 and 1. > > Likewise binary (and hence ternary etc.) sup and/or inf can be moved from > CABA to Set. Moving all finitary sup's for example turns Set into SLat > (semilattices, specifically of the meet kind) and CABA into StoneSLat, > aka algebraic lattices. > > By viewing Stone topology as the manifestation of infinite sup's and > inf's, the duality of Stone (Stone spaces) and Bool (Boolean algebras) > can be understood as the migration of the infinitary sup's and inf's > of CABA to Set, turning CABA into Bool and Set into Stone. From this > viewpoint the ability to present limits in Top follows by duality from > the optional removal in CABA of infinitary inf's to yield Top^op, while > Frm (frames) as Loc^op (locales) tightens this up by removing "optional". > > Chu(Set,2) provides a uniform setting for this rule. All the above > categories C have a "common" full concrete embedding in Chu(Set,2) > in which the points remain unchanged (concreteness) while the states > or opens are taken to be the morphisms of C to the realization of the > schizophrenic object 2 as an object of C. In this setting the above > tendency (but not the converse part) can be made a theorem about Chu > spaces over 2 as follows, at least for the finitary operations. > > Theorem 0: If a space A has constant 0 then its dual A\perp does not > have constant 1 (and dually with 0 and 1 interchanged). > > Proof. A row of all 0's precludes a column of all 1's (the impossibility > of having an irresistible force and an immovable object). > > Theorem 2: If A has all binary joins then the only binary meets existing > in A\perp are of comparable elements. > > Proof. Suppose x,y are incomparable columns of A (points of A\perp) > whose meet x&y is a column of A. Then there exist rows a,b of A such that > > x y x&y > a 0 1 0 > b 1 0 0 > > is part of A's matrix. Now form the join of a and b: > > a|b 1 1 0 > > This contradicts x&y being the meet of x and y. QED > > (Apropos of the comparability issue, note that the category of finite > chains with bottom, with morphisms all monotone bottom-preserving > functions, is self-dual.) > > I don't know how to state the corresponding theorem if any for infinitary > sup's and inf's. And I have no idea how to generalize all this to > Chu(Set,3) and beyond. > > I became aware of this complementarity principle for opposite categories > around 1990, and contemplating it led my student Vineet Gupta and myself > to (ordinary) Chu spaces in 1992, at which point we learned that they > were not new (but not well known). > > Vaughan Pratt --------------9DA47DF35DB9657A80A57DB9 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit A category is called " left " if it has a strict initial object and any map with an initial domain is regular (in the general sense). The opposite of a left category is called a " right " category. The key fact here is that a left category is never right unless it is trivial (i.e. any map is an isomorphism). Since may natural categories are either left or right, this enable us to introduce the "relative version" of a categorical concept with a dual. The following short note

On Left and Right Categories

is available at

www.azd.com/lrcat.html

which is inspired by Vaughan Pratt comments:

Vaughan Pratt wrote:

From: "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
>I can't see any sense in which the opposite of a
>category can be regarded as complementary to it.

Peter's book "Stone spaces" (CUP 1982) studies many categories that
obey the rule that the signature of the opposite of C is the complement
of the signature of C, with respect to both existence and direction
of sup's and inf's of cardinalities 0, finite nonzero, and infinite.
Namely, if sup's of a given arity exist in C then inf's of that arity
do not exist in C^op, and conversely (at least in the examples).

The extremal pair of opposite categories in this regard are CABA,
complete atomic Boolean algebras, which has all inf's and sup's, dual to
Set having none (but for this purpose we could as well take StoneDLat,
dual to Poset).  "In the middle" is CSLat, complete semilattices,
having sup's of all cardinalities and no inf's, dual to itself via a
duality that interchanges sup's and inf's (not to be confused with the
equivalence that performs this interchange).

Top and bottom as zeroary sup and inf can be moved independently from
CABA to Set to give pointed and bipointed sets dual to CABA's lacking
one or both constants 0 and 1.

Likewise binary (and hence ternary etc.) sup and/or inf can be moved from
CABA to Set.  Moving all finitary sup's for example turns Set into SLat
(semilattices, specifically of the meet kind) and CABA into StoneSLat,
aka algebraic lattices.

By viewing Stone topology as the manifestation of infinite sup's and
inf's, the duality of Stone (Stone spaces) and Bool (Boolean algebras)
can be understood as the migration of the infinitary sup's and inf's
of CABA to Set, turning CABA into Bool and Set into Stone.  From this
viewpoint the ability to present limits in Top follows by duality from
the optional removal in CABA of infinitary inf's to yield Top^op, while
Frm (frames) as Loc^op (locales) tightens this up by removing "optional".

Chu(Set,2) provides a uniform setting for this rule.  All the above
categories C have a "common" full concrete embedding in Chu(Set,2)
in which the points remain unchanged (concreteness) while the states
or opens are taken to be the morphisms of C to the realization of the
schizophrenic object 2 as an object of C.  In this setting the above
tendency (but not the converse part) can be made a theorem about Chu
spaces over 2 as follows, at least for the finitary operations.

Theorem 0: If a space A has constant 0 then its dual A\perp does not
have constant 1 (and dually with 0 and 1 interchanged).

Proof.  A row of all 0's precludes a column of all 1's (the impossibility
of having an irresistible force and an immovable object).

Theorem 2: If A has all binary joins then the only binary meets existing
in A\perp are of comparable elements.

Proof.  Suppose x,y are incomparable columns of A (points of A\perp)
whose meet x&y is a column of A.  Then there exist rows a,b of A such that

             x  y  x&y
        a    0  1   0
        b    1  0   0

is part of A's matrix.  Now form the join of a and b:

       a|b   1  1   0

This contradicts x&y being the meet of x and y.  QED

(Apropos of the comparability issue, note that the category of finite
chains with bottom, with morphisms all monotone bottom-preserving
functions, is self-dual.)

I don't know how to state the corresponding theorem if any for infinitary
sup's and inf's.  And I have no idea how to generalize all this to
Chu(Set,3) and beyond.

I became aware of this complementarity principle for opposite categories
around 1990, and contemplating it led my student Vineet Gupta and myself
to (ordinary) Chu spaces in 1992, at which point we learned that they
were not new (but not well known).

Vaughan Pratt

  --------------9DA47DF35DB9657A80A57DB9-- From cat-dist Wed Jul 8 14:09:11 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA13729 for categories-list; Wed, 8 Jul 1998 13:07:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 8 Jul 1998 08:23:20 -0400 (EDT) Subject: categories: xxx preprint archive From: James Stasheff To: categories@mta.ca cc: dmd1@lehigh.edu, eprint-discussion@math.duke.edu Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The figures are in for this years submissions to the math archive at xxx.lanl.gov '98 Total: 1022 AG 221; QA 191; DG 110; MP 95; GT 70; CO 54; OA 32; CV 30; PR 30; FA 24; SP 24; RT 19; DS 15; AT 14; AP 11; NT 11; CA 10; GR 10; LA 9; RA 7; KT 6; LO 5; MG 5; IG 4; SG 4; GN 3; NA 3; HO 2; SC 2; CT 1; Is it really true that algebraic geoemtry is flourishing that much better than algebraic topology not to mention CT = category theory!! If you are unfamiliar with the archive, try to xxx.lanl.gov home page or contact me. ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Wed Jul 8 14:10:31 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA12756 for categories-list; Wed, 8 Jul 1998 13:06:36 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Koslowski Message-Id: <199807081110.NAA29194@lisa.iti.cs.tu-bs.de> Subject: categories: re: co- To: categories@mta.ca (categories list) Date: Wed, 8 Jul 1998 13:10:05 +0200 (MET DST) X-Mailer: ELM [version 2.4ME+ PL28 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Ross Street brought up an important point. As you start considering higher-dimensional categories, the number of possible dualizations rises exponentially. Also, given a monoidal category V, we can consider it either as a bicategory with trivial hom-categories, or as a one-object bicategory (usually called the suspension of V). Which of these views should be "notationally invariant"? Should colimits in Set be oplimits in the supension of Set? Best regards, -- J"urgen P.S. Why are certain categorical notions preferred over their dual counterparts? E.g., hardly anyone talks about the Yoneda embedding of A into [A,Set]^op. -- J"urgen Koslowski % If I don't see you no more in this world ITI % I meet you in the next world TU Braunschweig % and don't be late! koslowj@iti.cs.tu-bs.de % Jimi Hendrix (Voodoo Child) From cat-dist Wed Jul 8 14:13:00 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA00540 for categories-list; Wed, 8 Jul 1998 13:08:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 8 Jul 1998 15:06:26 +0100 (BST) From: Achim Jung X-Sender: axj@wallace To: categories@mta.ca Subject: categories: Lectureship in Birmingham Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The University of Birmingham School of Computer Science TEMPORARY LECTURER IN COMPUTER SCIENCE This post has arisen through a one year leave of absence granted to Dr de Paiva. Applications in the area of Theoretical Computer Science will be treated preferentially but applicants from other areas will also be considered. There may be an opportunity to extend this post beyond one year. The teaching duties connected with this appointment will include a two semester introduction to computing for students in the Faculty of Arts. Applicants should have or be about to complete a PhD in Computer Science or a closely related field, or should have equivalent research experience. Application forms (returnable by 31 July 1998) and further particulars available from: The Director of Staffing Services The University of Birmingham Edgbaston, Birmingham, B15 2TT tel: +44 (0)121 414 6486 (24 hours) email: staffing@bham.ac.uk Please quote reference 13669. Informal enquiries to: Prof Achim Jung tel: +44 (0)121 414 4776 email: A.Jung@cs.bham.ac.uk See also: http://www.cs.bham.ac.uk/school/jobvacancies.html Working towards equal opportunities. From cat-dist Wed Jul 8 14:24:23 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA14463 for categories-list; Wed, 8 Jul 1998 13:09:37 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 08 Jul 1998 17:52:11 +0200 From: Eva Ullan Subject: categories: CSL'99 First Call for Papers (Text and LaTex Versions) X-Sender: evah@147.96.1.121 To: categories@mta.ca Message-id: MIME-version: 1.0 Content-type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id MAA10256 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: ____________________________________________________ My apologies if you receive this more than once! ____________________________________________________ =================================== 1st CALL FOR PAPERS -- CSL'99 Annual Conference of the European Association for Computer Science Logic September 20-24, 1999, Madrid, Spain =================================== CSL is the annual conference of the European Association for Computer Science Logic (EACSL). The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. Suggested, but not exclusive, topics of interest include: * abstract datatypes, * automated deduction, * categorical and topological approaches, * concurrency theory, * constructive mathematics, * database theory, * domain theory, * finite model theory, * lambda and combinatory calculi, * logical aspects of computational complexity, * logical foundations of programming paradigms, * linear logic, * modal and temporal logics, * model checking, * program logics and semantics, * program specification, transformation and verification, * rewriting, * symbolic computation. EACSL BOARD Marc Bezem (President) Ian Stewart (Vice-President) Clemens Lautemann (Treasurer) PROGRAM COMMITEE Samson Abramsky (Edinburgh, UK) Marc Bezem (Utrecht, The Netherlands) Peter Clote (Munich, Germany) Hubert Comon (Cachan, France) Jorg Flum (Freiburg i.Br., Germany) (co-chair) Harald Ganzinger (Saarbrucken, Germany) Neil Immerman (Amherst, USA) Neil Jones (Copenhagen, Denmark) Jan Maluszynski (Linkoping, Sweden) Michael Maher (Brisbane, Australia) Catuscia Palamidessi (Pennsylvania, USA) Mario Rodriguez-Artalejo (Madrid, Spain) (co-chair) Wolfgang Thomas (Aachen, Germany) Jerzy Tiuryn (Warsaw, Poland) Glynn Winskel (Aarhus, Denmark) Martin Wirsing (Munich, Germany) LOCAL ORGANIZING COMMITTEE J. Carlos Gonzalez-Moreno Teresa Hortala-Gonzalez Javier Leach-Albert (chair) Paco Lopez-Fraguas Fernando Saenz-Perez Eva Ullan-Hernandez SCIENTIFIC PROGRAMME In addition to invited lectures and contributed papers, there will be two tutorials on theorem proving and rewriting techniques, scheduled on september 24 afternoon (Friday) and september 25 morning(Saturday), immediately after the main conference. ** September 20--24, 1999: Invited Lectures and Contributed Papers The list of invited speakers will include: Jose Luis Balcazar (Barcelona, Spain) Javier Esparza (Munich, Germany) Martin Grohe (Freiburg, Germany) Peter D. Mosses (Aarhus, Denmark) V. Vianu (San Diego, USA) ** September 24--25, 1999: CSL Tutorials Douglas Howe (Bell Labs, USA) Aart Middeldorp (Tsukuba, Japan) PAPER SUBMISSIONS Submitted papers must describe work not previously published. They must not be submitted concurrently to a journal or to another conference. Papers authored or coauthored by members of the Program Committee are not allowed. Submissions must not exceed 15 pages (in the usual format for Springer LNCS), including title page, figures and references. The title page must contain: title and authors; physical and e-mail addresses; telephone and (if available) fax number for each author; identification of corresponding author, if not the first author; an abstract of no more than 200 words; a list of keywords. Submissions must arrive by April 2, 1999, and notifications of acceptance will be sent by July 5, 1999. Authors are invited to send manuscripts by electronic mail, as uuencoded gzipped postcript files: * see the conference home page for instructions http://mozart.sip.ucm.es:1580/csl99 (forthcoming) * or send an empty message with subject "submission information'' to csl99org@eucmos.sim.ucm.es Those authors without access to the facilities for electronic submission can alternatively submit five hardcopies to: Prof. Mario Rodriguez Artalejo, CSL'99 Departamento de Sistemas Informaticos y Programacion Facultad de Matematicas, Universidad Complutense de Madrid Av. Complutense s/n E-28040 Madrid Spain E-mail: mario@sip.ucm.es Phone: +34 1 3 94 45 12 Fax: +34 1 3 94 46 07 PUBLICATION According to the current EACSL policy, authors of accepted papers must present them at the conference and simultaneously submit a revised full version to be considered in a second refereeing process. Papers accepted in this second round will appear in a proceedings volume published by Springer in the Lecture Notes in Computer Science series, after the conference. This policy might be changed after the EACSL membership assembly at CSL'98 (Brno, Czech Republic, August 23-28, 1998). New information will be given in the 2nd call for papers, to be sent out in coming september. IMPORTANT DATES Paper submissions April 2, 1999 Notifications of acceptance July 5, 1999 CSL'99 main conference September 20-24, 1999 CSL'99 Tutorials September 24-25, 1999 ADDITIONAL INFORMATION CSL'99 home page: http://mozart.sip.ucm.es:1580/csl99 (forthcoming) CSL'99 local organization: csl99org@eucmos.sim.ucm.es % ----------------------- LaTex Version ------------------------------------ % 1st Call for Papers, CSL'99. % Last revision: June 30, 1998. \documentstyle{article} \oddsidemargin 6pt \evensidemargin 6pt \marginparwidth 90pt \marginparsep 10pt \topmargin -30pt \headheight 12pt \headsep 25pt \footheight 12pt \footskip 30pt \columnsep 10.5pt \columnseprule 0pt \addtolength{\oddsidemargin}{-2.3cm} \setlength{\textwidth}{18.7cm} \addtolength{\topmargin}{-1cm} \setlength{\textheight}{27cm} \pagestyle{empty} \begin{document} % Heading \begin{center} {\large \bf 1st CALL FOR PAPERS -- CSL'99} \end{center} \begin{center} {\Large \bf Annual Conference of the }\\[1.5ex] {\Large \bf European Association for Computer Science Logic} \end{center} \begin{center} {\large \bf Madrid, Spain, September 20-24, 1999} \end{center} \vspace*{0.15in} % Left column \parbox[t]{6.5cm}{ \footnotesize \noindent {\small \bf EACSL Board:} \vspace*{0.1in} \begin{tabular}{l} Marc Bezem (President)\\[0.7ex] Ian Stewart (Vice-President)\\[0.7ex] Clemens Lautemann (Treasurer) \end{tabular} \vspace*{0.20in} \noindent {\small \bf Program Committee:} \vspace*{0.1in} \begin{tabular}{l} Samson Abramsky (Edinburgh, UK)\\[0.7ex] Marc Bezem (Utrecht, The Netherlands)\\[0.7ex] Peter Clote (Munich, Germany)\\[0.7ex] Hubert Comon (Cachan, France)\\[0.7ex] J\"{o}rg Flum (Freiburg i.Br., Germany) \\ \hspace{1cm} ({\bf co-chair})\\[0.7ex] Harald Ganzinger (Saarbr\"{u}cken, Germany)\\[0.7ex] Neil Immerman (Amherst, USA)\\[0.7ex] Neil Jones (Copenhagen, Denmark)\\[0.7ex] Jan Maluszynski (Link\"{o}ping, Sweden)\\[0.7ex] Michael Maher (Brisbane, Australia)\\[0.7ex] Catuscia Palamidessi (Pennsylvania, USA)\\[0.7ex] Mario Rodr\'{\i}guez-Artalejo (Madrid, Spain) \\ \hspace{1cm} ({\bf co-chair})\\[0.7ex] Wolfgang Thomas (Aachen, Germany)\\[0.7ex] Jerzy Tiuryn (Warsaw, Poland)\\[0.7ex] Glynn Winskel (Aarhus, Denmark)\\[0.7ex] Martin Wirsing (Munich, Germany) \end{tabular} \vspace*{0.20in} \noindent {\small \bf Invited Speakers:} \vspace*{0.1in} \begin{tabular}{l} Jos\'{e} Luis Balc\'{a}zar (Barcelona, Spain)\\[0.7ex] Javier Esparza (Munich, Germany)\\[0.7ex] Martin Grohe (Freiburg, Germany)\\[0.7ex] Peter D. Mosses (Aarhus, Denmark)\\[0.7ex] V. Vianu (San Diego, USA) \end{tabular} \vspace*{0.20in} \noindent {\small \bf Tutorialists:} \vspace*{0.1in} \begin{tabular}{l} Douglas Howe (Bell Labs, USA)\\[0.7ex] Aart Middeldorp (Tsukuba, Japan) \end{tabular} \vspace*{0.20in} \noindent {\small \bf Local Organizing Committee:} \vspace*{0.1in} \begin{tabular}{l} J. Carlos Gonz\'{a}lez-Moreno\\[0.7ex] Teresa Hortal\'{a}-Gonz\'{a}lez\\[0.7ex] Javier Leach-Albert ({\bf chair})\\[0.7ex] Paco L\'{o}pez-Fraguas\\[0.7ex] Fernando S\'{a}enz-P\'{e}rez\\[0.7ex] Eva Ull\'{a}n-Hern\'{a}ndez \end{tabular} } % \end{parbox} % Right column. No blank line here! \parbox[t]{5mm}{ \rule[-21.8cm]{0.2mm}{22.1cm} } %\end{parbox} \begin{minipage}[t]{11.0cm} \small {\bf Aims and Scope of the Conference:} {\bf CSL} is the annual conference of the {\em European Association for Computer Science Logic} (EACSL). The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. Suggested, but not exclusive, topics of interest include: abstract datatypes, automated deduction, categorical and topological approaches, concurrency theory, constructive mathematics, database theory, domain theory, finite model theory, lambda and combinatory calculi, logical aspects of computational complexity, logical foundations of programming paradigms, linear logic, modal and temporal logics, model checking, program logics and semantics, program specification, transformation and verification, rewriting, symbolic computation. \vspace*{0.15in} \noindent {\bf Scientific Programme:} In addition to invited lectures and contributed papers, there will be two tutorials on theorem proving and rewriting techniques, scheduled on September 24 afternoon (Friday) and September 25 morning (Saturday), immediately after the main conference. \vspace*{0.15in} \noindent {\bf Paper Submissions:} Submitted papers must describe work not previously published. They must not be submitted concurrently to a journal or to another conference. Papers authored or coauthored by members of the Program Committee are not allowed. Submissions must not exceed 15 pages (in the usual format for Springer LNCS), including title page, figures and references. The title page must contain: title and authors; physical and e-mail addresses; telephone and (if available) fax number for each author; identification of corresponding author, if not the first author; an abstract of no more than 200 words; a list of keywords. Submissions must arrive by {\bf April 2, 1999}, and notifications of acceptance will be sent by {\bf July 5, 1999}. Authors are invited to send manuscripts by electronic mail, as uuencoded gzipped postcript files (see the conference home page for instructions, or send an empty message with subject ``submission information'' to csl99org@eucmos.sim.ucm.es). Those authors without access to the facilities for electronic submission can alternatively submit {\em five hardcopies} to: \vspace*{0.05in} \begin{tabular}{l} Prof. Mario Rodr\'{\i}guez-Artalejo, CSL'99 \\ Departamento de Sistemas Inform\'{a}ticos y Programaci\'{o}n \\ Facultad de Matem\'{a}ticas, Universidad Complutense de Madrid \\ Av. Complutense s/n ~~~~~~~~~~ Phone: +34 1 3 94 45 12 \\ E-28040 Madrid ~~~~~~~~~~~~~~~~~ Fax: +34 1 3 94 46 07 \\ Spain ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ E-mail: mario@sip.ucm.es \end{tabular} \vspace*{0.15in} \noindent {\bf Publication:} According to the current EACSL policy, authors of accepted papers must present them at the conference and simultaneously submit a revised full version to be considered in a second refereeing process. Papers accepted in this second round will appear in a proceedings volume published by Springer in the Lecture Notes in Computer Science series, after the conference. This policy might be changed after the EACSL membership assembly at CSL'98 (Brno, Czech Republic, August 23-28, 1998). New information will be given in the 2nd call for papers, to be sent out in coming September. \vspace*{0.15in} \noindent {\bf Important Dates:} \begin{tabular}{ll} April 2, 1999 & Paper submissions\\ July 5, 1999 & Notifications of acceptance\\ September 20-24, 1999 & CSL'99 main conference\\ September 24-25, 1999 & CSL'99 Tutorials \end{tabular} \vspace*{0.15in} \noindent {\bf Additional Information:} \vspace{0.8mm} \begin{tabular}{ll} CSL'99 home page: & http://mozart.sip.ucm.es:1580/csl99 {\scriptsize (forthcoming)} \\ CSL'99 local organization: & E-mail: csl99org@eucmos.sim.ucm.es \end{tabular} \end{minipage} \end{document} From cat-dist Wed Jul 8 23:31:20 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA01680 for categories-list; Wed, 8 Jul 1998 22:46:56 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807081805.LAA17558@coraki.Stanford.EDU> To: categories@mta.ca Subject: categories: Re: xxx preprint archive In-reply-to: Your message of "Wed, 08 Jul 1998 08:23:20 -0400." Date: Wed, 08 Jul 1998 11:05:31 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: >Is it really true that algebraic geoemtry is flourishing that much better >than algebraic topology not to mention CT = category theory!! The number of submissions to xxx.lanl.gov seems more driven by culture than anything else. The following are the number of submissions for 1998 to date: Astrophysics: 2225 Condensed Matter 2272 + 10 more physics areas Mathematics (total) 932 Computation & Language 48 Evidently very few computer scientists think to submit to xxx.lanl.gov. I wouldn't infer from those numbers that computer science is not flourishing or publishing. As far as algebraic geometry vs category theory goes, the most recent 5 submissions in those respective areas span 1 week vs. 11 weeks, suggesting that the recent rate of submissions is closer to 11:1 than 221:1. (I'd have taken a larger sample if one had been as handy as the most-recent-5 statistic.) Vaughan Pratt From cat-dist Wed Jul 8 23:31:24 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA08370 for categories-list; Wed, 8 Jul 1998 22:50:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Greg Kuperberg Message-Id: <199807081913.MAA15529@matching.math.ucdavis.edu> Subject: Re: categories: xxx preprint archive To: categories@mta.ca Date: Wed, 8 Jul 1998 12:13:26 -0700 (PDT) In-Reply-To: from "John R Isbell" at Jul 8, 98 03:01:20 pm Content-Type: text Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: > Jim, > There is something wrong (probably internal at > xxx.lanl.gov) with your table of '98 abstracts in > various branches of math. I went there (for the > first time, thanks for the address) and clicked > on Category Theory and found 5 abstracts. Those > were all from the 3 months preceding this month, > so I thought there should be more in '98. I did > a search for the words 'category theory', > limited to '98, and got 8 abstracts. However, > more than half of those were classified, > primarily, as Quantum Groups or something. So > God only knows how many CT's there are in lanl > in '98, but not less than 5. There is 1 with primary category CT and 7 cross-listed into CT in 1998. A second CT paper dated 1995 is from the migration of the MSRI preprint series. Jim's table, which was forwarded from xxx staff, counts only primary submissions, to avoid double-counting. You can get a clear picture at http://front.math.ucdavis.edu/math.CT I should say that the main consequences so far of creating CT has been a lot of theorizing about the categories in the xxx mathematics archive. Perhaps that's a natural response from category theorists, but it's not what the people who created CT had in mind. Greg From cat-dist Wed Jul 8 23:35:06 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA03833 for categories-list; Wed, 8 Jul 1998 22:51:04 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 08 Jul 1998 14:39:02 -0500 (EST) From: Fred E J Linton Subject: categories: RE: co- To: Koslowski , Categories Message-id: <98070819390243/0004142427PV1EM@mcimail.com> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Hi, all, Jurgen asks: > Why are certain categorical notions preferred over their dual > counterparts? E.g., hardly anyone talks about the Yoneda embedding > of A into [A,Set]^op. One point of my old (alas still unpublished) remarks "Sur les choix de variance predestinees" was exactly why one "should" only see those Yoneda maps in the forms A ---> [A,Set]^op -- and A ---> [A^op, Set] -- but no others (!). [First Ehresmann conf., Paris/Fontainebleau, 197?.] -- Fred From cat-dist Wed Jul 8 23:43:32 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA27958 for categories-list; Wed, 8 Jul 1998 22:54:07 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 9 Jul 1998 10:19:08 +1000 (EST) From: Sjoerd Erik CRANS Message-Id: <199807090019.KAA06825@krakatoa.mpce.mq.edu.au> To: categories@mta.ca Subject: categories: Re: xxx preprint archive X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: James Stasheff wrote: > The figures are in for this years submissions to the math archive at > xxx.lanl.gov > > > '98 Total: 1022 > AG 221; QA 191; DG 110; MP 95; GT 70; CO 54; OA 32; CV 30; PR 30; FA 24; > SP 24; > RT 19; DS 15; AT 14; AP 11; NT 11; CA 10; GR 10; LA 9; RA 7; KT 6; LO 5; > MG 5; > IG 4; SG 4; GN 3; NA 3; HO 2; SC 2; CT 1; > > Is it really true that algebraic geoemtry is flourishing that much better > than algebraic topology not to mention CT = category theory!! Although this might indeed well be true, isn't is a bit too simplistic to measure the succes of a subject this way? I think that for a more balanced view it is useful to consider the following points: 1. CT is a new subject class, and naturally has lower traffic than the well established ones, 2. There are cross references to CT from other classes, 3. There are papers containing some category theory classified under other classes; some of these could well have been classified CT (remember that the author determines the subject class!), 4. The position of Category Theory in Mathematics is quite different from Algebraic Geometry's (more marginal??), 5. The categorical community is relatively small, so categorists might be thinking they don't need a preprint archive, 6. Category Theory is less "time-sensitive" than other subjects, so categorists don't rush off to get their preprints time-stamped (as I have heard rumoured is the practice among (mathematical) physicists), 7. And there's the compulsory-tex-source-submission issue ... Sjoerd Crans School of MPCE Macquarie University NSW 2109 Australia email: scrans@mpce.mq.edu.au From cat-dist Thu Jul 9 09:53:13 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA07946 for categories-list; Thu, 9 Jul 1998 08:48:25 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807090404.VAA19711@coraki.Stanford.EDU> To: Categories Subject: categories: RE: co- In-reply-to: Your message of "Wed, 08 Jul 1998 14:39:02 -0500." <98070819390243/0004142427PV1EM@mcimail.com> Date: Wed, 08 Jul 1998 21:04:34 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: From: Fred E J Linton >One point of my old (alas still unpublished) remarks "Sur les choix de variance >predestinees" was exactly why one "should" only see those Yoneda maps in the >forms A ---> [A,Set]^op -- and A ---> [A^op, Set] -- but no others (!). >[First Ehresmann conf., Paris/Fontainebleau, 197?.] Mildly apropos of this, the two maps can be rolled into one, in a sense, to give the "bi-Yoneda embedding" F:C->Chu(Set,|C|) that I presented at the Barrfest, where |C| denotes the set of arrows of C. This embedding represents each object b of C as the Chu space F(b) = (A,r,X), r:AxX->K, where A is the set of arrows f:a->b over all a, X is the set of arrows h:b->c over all c, and r(f,h) = hf. Each morphism g:b->b' is represented as the pair F(g) = (j,k) of functions j:F_A(b)->F_A(b'), k:F_X(b')->F_X(b) defined by j(f) = gf, k(h) = hg for each point f:a->b in F_A(b) and state h:b'->c in F_X(b'). (j,k) is a Chu transform (= continuous, = satisfies the adjointness condition). F is full, faithful, concrete with respect to U:C->Set defined by U(b) {f:a->b} ("left" Yoneda), and co-concrete with respect to V:C->Set^op defined by V(b) = {h:b->c} ("right" Yoneda) (or the other way round depending on which way you're facing). Regrettably this didn't go in the proceedings, being already committed to TCS. Vaughan Pratt From cat-dist Thu Jul 9 14:56:13 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA32319 for categories-list; Thu, 9 Jul 1998 13:41:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807090525.WAA20214@coraki.Stanford.EDU> To: categories@mta.ca Subject: categories: Re: A sense in which C^op is complementary to C In-reply-to: Your message of "Tue, 07 Jul 1998 15:27:14 -0400." <35A27691.CEAF45BC@iswest.com> Date: Wed, 08 Jul 1998 22:25:50 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: From: Zhaohua Luo >A category is called " left " if it has a strict initial object and any map >with an initial domain is regular (in the general sense). The opposite of a >left category is called a " right " category. This division of categories into left, right, and other caters for only a very special case of the general phenomenon "signature of opposite is complement of signature", namely where *all* the algebra is on the right, call this C\op. The more general situation permits the algebra to be split between C and C\op, e.g. CSLat which puts the sups (say) in C and sends the infs off to C\op, which turn into sups as they "pass through the mirror." Many other partitions of algebra are possible that similarly do not fit this left-right classification and so fall under "other". Vaughan Pratt From cat-dist Thu Jul 9 14:56:53 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA31557 for categories-list; Thu, 9 Jul 1998 13:54:44 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 8 Jul 1998 15:01:20 -0400 (EDT) From: John R Isbell To: James Stasheff cc: categories@mta.ca Subject: categories: Re: xxx preprint archive In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: [note from moderator: a response to this has been posted, but the original was inadvertently delayed] Jim, There is something wrong (probably internal at xxx.lanl.gov) with your table of '98 abstracts in various branches of math. I went there (for the first time, thanks for the address) and clicked on Category Theory and found 5 abstracts. Those were all from the 3 months preceding this month, so I thought there should be more in '98. I did a search for the words 'category theory', limited to '98, and got 8 abstracts. However, more than half of those were classified, primarily, as Quantum Groups or something. So God only knows how many CT's there are in lanl in '98, but not less than 5. John From cat-dist Thu Jul 9 15:54:10 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id PAA28814 for categories-list; Thu, 9 Jul 1998 15:00:53 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <199807091409.LAA19397@mailserv.mta.ca> To: categories@mta.ca Subject: categories: RA-position in Birmingham Date: Thu, 09 Jul 1998 14:59:09 +0100 From: Eike Ritter Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The University of Birmingham School of Computer Science POSTDOCTORAL RESEARCH FELLOW IN FUNCTIONAL PROGRAMMING Applications are invited for a Postdoctoral Research Fellow to work for 16 months on an EPSRC-funded project "XSLAM: The eXplicit Substitutions Linear Abstract Machine". The investigators of this project are Dr Eike Ritter and Dr Valeria de Paiva. Applicants should have a PhD in Computer Science or Mathematics and ideally have knowledge of one or more of the following areas: functional programming, type theory, logic, and category theory. Application forms (returnable by 30 July 1998) and further particulars available from: The Director of Staffing Services The University of Birmingham Edgbaston, Birmingham, B15 2TT tel: +44 (0)121 414 6486 (24 hours) email: staffing@bham.ac.uk Please quote reference S13958/98 Informal enquiries to: Dr Eike Ritter tel: +44 (0)121 414 4772 email: E.Ritter@cs.bham.ac.uk See also: http://www.cs.bham.ac.uk/school/jobvacancies.html Working towards equal opportunities. From cat-dist Thu Jul 9 15:54:21 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id PAA05055 for categories-list; Thu, 9 Jul 1998 15:03:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 9 Jul 1998 12:11:57 -0400 (EDT) From: James Stasheff To: categories@mta.ca Subject: categories: p.s. Re: xxx preprint archive Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I may have given the wrong impression: Ginsparg writes: note that "Computation & Language" is not a comprehensive archive for all of Computer Science and all of Linguistics. it is a small archive started in '94, corresponding to just a small subject class of computer science, devoted to a very specific sub-area involving language. as such note that later this month we *will* be starting a comprehensive cs archive along the lines of what was done in math, and its advisory board, formed from an ACM committee early this year, has repeated many of the deliberations regarding the most effective partitioning, and its relation to the existing ACM classification scheme. (in the end the primary level is likely to reflect instead their conference structure.) the aim is to evolve that much more quickly to a set of mirrored comprehensive resources for physics, math and computer science -- presuming the latter two eventually choose to participate at the same level as the former... it is partly true that these are culture driven, but these cultures evolve: the examples of Astrophysics and Condensed Matter both started quite slowly six years ago (in comparison to High Energy Physics which took off instantly in '91 and saturated by late '93, essentially 100% participation) but those two each more than doubled their submission rates from '94-'96 and have continued (though Astrophysics is now nearing saturation as well), so these cultures are capable of adapting if it suits their research purposes. pg From cat-dist Mon Jul 13 12:33:28 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA10533 for categories-list; Mon, 13 Jul 1998 11:11:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from NIEVAX.nie.ac.sg (nievax.nie.ac.sg [155.69.33.1]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id DAA29386 for ; Mon, 13 Jul 1998 03:38:27 -0300 (ADT) X-Received: from mr.nie.ac.sg by nievax.nie.ac.sg (PMDF V5.0-4 #7636) id <01IZCRHT3XKW000H9B@nievax.nie.ac.sg> for cat-dist@mta.ca; Mon, 13 Jul 1998 13:56:33 +0800 X-Received: with PMDF-MR; Mon, 13 Jul 1998 11:12:57 +0800 MR-Received: by mta IE002.MUAS; Relayed; Mon, 13 Jul 1998 11:12:57 +0800 MR-Received: by mta IE002; Relayed; Mon, 13 Jul 1998 19:12:58 +0800 Disclose-recipients: prohibited Date: Mon, 13 Jul 1998 11:12:57 +0800 From: ZHAOD Subject: categories: Upper case and lower case In-reply-to: To: cat-dist Message-id: <2857121113071998/A12731/IE002/11C76ACC3800*@MHS.nie.ac.sg> Autoforwarded: false MIME-version: 1.0 Content-type: TEXT/PLAIN; CHARSET=US-ASCII Content-transfer-encoding: 7BIT Importance: normal UA-content-id: 11C76ACC3800 X400-MTS-identifier: [;2857121113071998/A12731/IE002] Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: In mathematics many structures are named after some one's name. For example, Boolean algebra, Hermitian matrices, Hausdorff space, Euclidean space. The first letters of the person's name are usually in upper case. The only exception I have seen are the abelian group and sober space. Does any one know why these two cases are different from others? Thanks Zhao Dongsheng From cat-dist Mon Jul 13 17:15:19 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA28594 for categories-list; Mon, 13 Jul 1998 16:03:09 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 13 Jul 1998 16:37:43 +0100 (BST) From: Paul Taylor Message-Id: <199807131537.QAA28460@ruby.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: Upper case and lower case Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: > In mathematics many structures are named after some one's name. A questionable practice in many cases, and not necessarily complimentary to the person concerned. For example, G. H. Hardy is famous in genetics for a rather trivial lemma in Bayesian statistics which was his answer to a question over High Table lunch in Trinity one day. How on earth is anyone meant to know what might be meant by "Gauss's Lemma/Theorem/etc"? On the other hand, things can be knocked off inappropriate pedestals by giving them eponymous names. For example, what others call "simple type theory" or "higher order intuitionistic logic" I call "Zermelo type theory" in my book. This has certainly given me a more balanced view of its (limited) importance in mathematics, and I hope to have the same effect on my readers. Given that you're doing it, whether to use a capital depends on national and linguistic custom. The German phrase "hilbertische Raum" looks very peculiar to me, for example. I was brought up to give people capital letters, whether they're nouns or adjectives. I tend *not* to do this if it seems to me that usage of the word has strayed rather a long way from what the person in question actually did, for example "cartesian transformation" for a natural transformation whose naturality squares are pullbacks. Peter Freyd, who of course comes from a different culture from me, will probably tell you his views. Paul From cat-dist Mon Jul 13 17:15:53 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA28252 for categories-list; Mon, 13 Jul 1998 16:04:03 -0300 (ADT) X-Received: from triples.math.mcgill.ca (barr@Triples.Math.McGill.CA [132.206.150.30]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id PAA27231 for ; Mon, 13 Jul 1998 15:16:32 -0300 (ADT) X-Received: from localhost (barr@localhost) by triples.math.mcgill.ca (8.8.5/8.6.10) with SMTP id OAA07880; Mon, 13 Jul 1998 14:18:53 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Mon, 13 Jul 1998 14:18:53 -0400 (EDT) From: Michael Barr To: ZHAOD cc: cat-dist Subject: categories: Re: Upper case and lower case In-Reply-To: <2857121113071998/A12731/IE002/11C76ACC3800*@MHS.nie.ac.sg> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: First off, sober (or sobre) is not an eponym (the fancy name for these). I often write boolean, hausdorff, and euclidean. You sometimes see Abelian. So there are no standards. Note that boolean, euclidean and abelian have adjectival endings (as does Hermitian), while hausdorff does not. In French and German, the two other languages I know somewhat, it is standard that all adjectives be in lower case, that is not so in English. So it comes down to a matter of convention and, basically, familiarity. In physics, it is considered a mark of great respect to achieve lower case status. Nearly all physical constants and units are lower case. But mathematicians do not accept standards conventions and journals make no attempt to enforce uniformity in these matters. On Mon, 13 Jul 1998, ZHAOD wrote: > > In mathematics many structures are named > after some one's name. For example, Boolean > algebra, Hermitian matrices, Hausdorff > space, Euclidean space. The first letters of > the person's name are usually in upper case. > The only exception I have seen are the > abelian group and sober space. Does any one > know why these two cases are different from > others? > > Thanks > > Zhao Dongsheng > > > From cat-dist Mon Jul 13 20:39:04 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA25228 for categories-list; Mon, 13 Jul 1998 19:54:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 13 Jul 1998 16:34:30 -0400 (EDT) From: James Stasheff To: Paul Taylor cc: categories@mta.ca Subject: categories: Re: Upper case and lower case In-Reply-To: <199807131537.QAA28460@ruby.dcs.qmw.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: and then there is the traditon of misassigning priority by nameing the concept ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Mon Jul 13 21:39:31 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA02104 for categories-list; Mon, 13 Jul 1998 19:55:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <35AA4D8D.2A40888D@iswest.com> Date: Mon, 13 Jul 1998 14:10:21 -0400 From: Zhaohua Luo X-Mailer: Mozilla 4.05 [en] (Win95; I) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: abstract algebraic geometry Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The following short note (see the abstract below) Atomic Categories is available on Categorical Geometry Homepage at the following address: http://www.azd.com Note that to read the special symbols on these pages requires a viewer under Win95. (thanks to Vaughan Pratt for bringing this to my attention). Please let me know if you would like to have a copy in dvi format. Z. Luo ------------------------------------------------------------------------------------- Atomic Categories Zhaohua Luo Abstract: Let C be a category with a strict initial object 0. A map is called "non-initial" if its domain is not an initial object. A non-initial object T is called "unisimple" if for any two non-initial maps f: X --> T and g: Y --> T there are non-initial maps r: R --> X and s: R --> Y such that fr = gs. We say that C is an "atomic category" if any non-initial object is the codomain of a map with a unisimple domain. Many natural (left) categories arising in geometry are atomic (such as the categories of sets, topological spaces, posets, coherent spaces, Stone spaces, schemes, local ringed spaces, etc.) In this short note we show that each atomic category carries a unique functor to the category of sets, which plays the traditional role of "underlying functor" in categorical geometry --------------84037E1FA36AB214A0902978 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit The following short note (see the abstract below)

Atomic Categories

is available on Categorical Geometry Homepage at the following address:

http://www.azd.com

Note that to read the special symbols on these pages requires a viewer under Win95. (thanks to Vaughan Pratt for bringing this to my attention). Please let me know if you would like to have a copy in dvi format.

Z. Luo
-------------------------------------------------------------------------------------
Atomic Categories

Zhaohua Luo

Abstract:

Let C be a category with a strict initial object 0. A map is called "non-initial" if its domain is not an initial object. A non-initial object T is called "unisimple" if for any two non-initial maps f: X --> T and g: Y --> T there are non-initial maps r: R --> X and s: R --> Y such that fr = gs. We say that C is an "atomic category" if any non-initial object is the codomain of a map with a unisimple domain. Many natural (left) categories arising in geometry are atomic (such as  the categories of sets, topological spaces, posets, coherent spaces, Stone spaces, schemes, local ringed spaces, etc.) In this short note we show that each atomic category carries a unique functor to the category of sets, which plays the traditional role of "underlying functor" in categorical geometry
 
 
  --------------84037E1FA36AB214A0902978-- From cat-dist Tue Jul 14 09:23:55 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA09397 for categories-list; Tue, 14 Jul 1998 08:02:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Real-To: Message-Id: <3.0.32.19980713204814.00e46d14@pop.apk.net> X-Sender: cwells@pop.apk.net X-Mailer: Windows Eudora Pro Version 3.0 (32) Date: Mon, 13 Jul 1998 20:48:20 -0400 To: categories@mta.ca From: Charles Wells Subject: categories: Re: Upper case and lower case Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: > In mathematics many structures are named >after some one's name. For example, Boolean >algebra, Hermitian matrices, Hausdorff >space, Euclidean space. The first letters of >the person's name are usually in upper case. >The only exception I have seen are the >abelian group and sober space. Does any one >know why these two cases are different from >others? Actually, many people write Abelian group and some people write cartesian product. I have seen boolean algebra, too. Sober spaces are not named after a person. A sober space is a topological space in which every closed subspace that is not the union of proper closed subspaces is the closure of exactly one point. If you are sober then what you see is really there and you don't see double! I heard someone give this explanation at a meeting but I don't know its history. Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html From cat-dist Wed Jul 15 13:28:41 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA11335 for categories-list; Wed, 15 Jul 1998 11:35:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 15 Jul 1998 11:25:51 +0200 From: tholen@univaq.it (Walter Tholen) Message-Id: <199807150925.LAA10955@univaq.it> To: categories@mta.ca Subject: categories: Hilbertraum Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Just a brief comment concerning Paul's recent posting. I don't know in which German text he found "hilbertischer Raum", it has at least one mistake in it! Usually one says Hilbertraum, like Banachraum, Frechetraum, etc. Also possible is Hilbertscher Raum (without "i" after t), and hilbertscher Raum may also be acceptable. As far as I remember (I have no relevant reference book at hand at my current location), the rule for making out of a name an adjective by adding sch (and the appropriate e, er - depending on declention) is to keep the capital of the name, unless the term has become absolutely standard (like abelsche Gruppe); to use the lower case is then regarded as an honour to the person in question (Abel). No more linguistics - Cheers, Walter. From cat-dist Wed Jul 15 13:29:10 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA14773 for categories-list; Wed, 15 Jul 1998 11:37:49 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 15 Jul 1998 10:50:34 -0300 From: Robert Dawson Subject: categories: Re: co- To: Paul Taylor , categories@mta.ca Message-id: <01IZFDDFR5IQ005U9E@HUSKY1.STMARYS.CA> MIME-version: 1.0 X-Mailer: Microsoft Internet Mail 4.70.1161 Content-type: text/plain; charset=ISO-8859-1 Content-transfer-encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: ---------- > From: Paul Taylor > To: categories@mta.ca > Subject: categories: co- > Date: Friday, July 03, 1998 8:39 AM > > What are the origins of the co- prefix, as in coproduct, coequaliser .., > and who established their use? > > Has anybody ever thought through and written down any guidelines on > which of a pair of dual concepts is co-? > > Who is reponsible for dropping this prefix from cofinal? Njectural answer: anybody who doesn't want the ncept to be nfused with "cofinal" in the topological sense, which is surely an older usage. (Is this rrect?) Robert Dawson From cat-dist Wed Jul 15 13:29:53 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA06050 for categories-list; Wed, 15 Jul 1998 11:37:06 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from christa.unh.edu (dvf@christa.unh.edu [132.177.137.10]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id LAA25351 for ; Tue, 14 Jul 1998 11:10:28 -0300 (ADT) X-Received: (from dvf@localhost) by christa.unh.edu (8.8.8/8.8.8) id KAA21760 for cat-dist@mta.ca; Tue, 14 Jul 1998 10:10:26 -0400 (EDT) From: David V Feldman Message-Id: <199807141410.KAA21760@christa.unh.edu> Subject: categories: Re: Upper case and lower case To: cat-dist@mta.ca Date: Tue, 14 Jul 1998 10:10:25 -0400 (EDT) X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: > In mathematics many structures are named > after some one's name. For example, Boolean > algebra, Hermitian matrices, Hausdorff > space, Euclidean space. The first letters of > the person's name are usually in upper case. > The only exception I have seen are the > abelian group and sober space. Does any one > know why these two cases are different from > others? > > Thanks > > Zhao Dongsheng > > > Fred Linton explains the term sober space this way: if you haven't been drinking you don't see double (so you don't want any pair of points belonging to the same set of open sets) and you certainly don't see any pink elements (irreducible closed sets with no generic point). David Feldman From cat-dist Thu Jul 16 18:08:06 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id RAA09585 for categories-list; Thu, 16 Jul 1998 17:05:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 15 Jul 1998 18:38:40 -0500 (EST) From: Fred E J Linton Subject: categories: RE: Upper case and lower case To: Categories Message-id: <98071523384075/0004142427PV1EM@mcimail.com> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: David Feldman erroneously credits to me an insight that is not mine, but Peter Johnstone's. Cf. {Topos Theory}, p. 230: > ... If we regard two distinct points having the same closure > as an instance of double vision (and an irreducible closed set with no > generic point as a species of pink elephant!), then the reason for the > term "sober space" will be apparent. (Thanks, David, but credit where credit is due.) -- Fred From cat-dist Fri Jul 17 06:09:12 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id GAA10268; Fri, 17 Jul 1998 06:09:12 -0300 (ADT) Date: Fri, 17 Jul 1998 06:09:12 -0300 (ADT) From: Categories List Message-Id: <199807170909.GAA10268@mailserv.mta.ca> X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: rrosebru Subject: BOUNCE categories@mta.ca: Approval required: Status: RO X-Status: >From rrosebru Fri Jul 17 06:09:10 1998 Received: from emu.dpmms.cam.ac.uk (exim@emu.dpmms.cam.ac.uk [131.111.24.1]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id GAA11712 for ; Fri, 17 Jul 1998 06:09:09 -0300 (ADT) Received: from [131.111.24.25] (helo=owl.dpmms.cam.ac.uk ident=exim) by emu.dpmms.cam.ac.uk with esmtp (Exim 1.950 #4) id 0yx6Vi-0001Mr-00; Fri, 17 Jul 1998 10:09:02 +0100 Received: from ptj by owl.dpmms.cam.ac.uk with local (Exim 1.950 #4) id 0yx6Vh-0005lx-00; Fri, 17 Jul 1998 10:09:01 +0100 Subject: Re: categories: RE: Upper case and lower case To: FEJLINTON/0004142427@MCIMAIL.COM (Fred E J Linton) Date: Fri, 17 Jul 1998 10:09:01 +0100 (BST) Cc: categories@mta.ca In-Reply-To: <98071523384075/0004142427PV1EM@mcimail.com> from "Fred E J Linton" at Jul 15, 98 06:38:40 pm X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: From: "Dr. P.T. Johnstone" > > David Feldman erroneously credits to me an insight that is not mine, but > Peter Johnstone's. Cf. {Topos Theory}, p. 230: > > > ... If we regard two distinct points having the same closure > > as an instance of double vision (and an irreducible closed set with no > > generic point as a species of pink elephant!), then the reason for the > > term "sober space" will be apparent. > > (Thanks, David, but credit where credit is due.) > > -- Fred > I can't claim the credit either: the wording above is mine, but I copied the idea from something written by Bill Lawvere. I can't now find the reference, but I think it may have been in his 1976 Chicago lecture notes on "Variable Sets, Etendu and Variable Structures in Topoi" (of which I no longer have a copy). Peter Johnstone From cat-dist Fri Jul 17 08:33:27 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA16906; Fri, 17 Jul 1998 08:33:27 -0300 (ADT) Date: Fri, 17 Jul 1998 08:33:27 -0300 (ADT) From: Categories List Message-Id: <199807171133.IAA16906@mailserv.mta.ca> X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: rrosebru Subject: BOUNCE categories@mta.ca: Approval required: Status: RO X-Status: >From rrosebru Fri Jul 17 08:33:25 1998 Received: from merlin.mat.uc.pt (merlin.mat.uc.pt [192.138.204.6]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id IAA14259 for ; Fri, 17 Jul 1998 08:33:14 -0300 (ADT) From: ct99@mat.uc.pt Received: from matpc17.mat.uc.pt (matpc17.mat.uc.pt [192.138.204.149]) by merlin.mat.uc.pt (8.9.0/8.9.0) with SMTP id MAA08118 for ; Fri, 17 Jul 1998 12:33:08 +0100 (WET DST) Message-Id: <3.0.5.32.19980717124138.007a08e0@mat.uc.pt> X-Sender: ct99@mat.uc.pt X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.5 (32) Date: Fri, 17 Jul 1998 12:41:38 +0100 To: categories@mta.ca Subject: preliminary announcement Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" =================================================================== PRELIMINARY ANNOUNCEMENT =================================================================== CT99 International Category Theory Meeting Department of Mathematics University of Coimbra Coimbra, Portugal July 19-24, 1999 The Department of Mathematics of the University of Coimbra is organizing an International Meeting on Category Theory to be held at the University of Coimbra, from 19th to 24th of July, 1999. The program will consist of conferences delivered by invited speakers and contributed short talks. Scientific Committee: -------------------- Jiri Adamek (Technische Universitat Braunschweig, Germany) Bernhard Banaschewski (McMaster University, Canada) Peter T. Johnstone (University of Cambridge, UK) Andre Joyal (Universite du Quebec a Montreal, Canada) F. William Lawvere (SUNY at Buffalo, USA) Ross Street (Macquarie University, Australia) Walter Tholen (York University, Canada) Organizing Committee: -------------------- Manuela Sobral (Universidade de Coimbra) Maria Manuel Clementino (Universidade de Coimbra) Jorge Picado (Universidade de Coimbra) Lurdes Sousa (Instituto Politecnico de Viseu) Goncalo Gutierres (Universidade de Coimbra) ------------------------------------------------------------------- School on Category Theory and Applications Department of Mathematics University of Coimbra Coimbra, Portugal July 13-17, 1999 In the framework of Centro Internacional de Matematica (http://www.cim.pt) the Department of Mathematics of the University of Coimbra is also organizing a School on Category Theory and Applications from 13th to 17th of July, 1999. This school will consist of the following intensive courses, at a postgraduate level: n-Categories by John Baez (University of California, USA) Algebraic Theories by M. Cristina Pedicchio (University of Trieste, Italy) Chu Spaces: duality as a common foundation for computation and mathematics by Vaughan Pratt (Stanford University, USA). ------------------------------------------------------------------- A detailed announcement of both events will be made in October. ------------------------------------------------------------------- For further information mailto:ct99@mat.uc.pt From cat-dist Fri Jul 17 14:59:07 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA26474 for categories-list; Fri, 17 Jul 1998 13:58:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: RE: Upper case and lower case To: FEJLINTON/0004142427@MCIMAIL.COM (Fred E J Linton) Date: Fri, 17 Jul 1998 10:09:01 +0100 (BST) Cc: categories@mta.ca In-Reply-To: <98071523384075/0004142427PV1EM@mcimail.com> from "Fred E J Linton" at Jul 15, 98 06:38:40 pm X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: From: "Dr. P.T. Johnstone" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: > > David Feldman erroneously credits to me an insight that is not mine, but > Peter Johnstone's. Cf. {Topos Theory}, p. 230: > > > ... If we regard two distinct points having the same closure > > as an instance of double vision (and an irreducible closed set with no > > generic point as a species of pink elephant!), then the reason for the > > term "sober space" will be apparent. > > (Thanks, David, but credit where credit is due.) > > -- Fred > I can't claim the credit either: the wording above is mine, but I copied the idea from something written by Bill Lawvere. I can't now find the reference, but I think it may have been in his 1976 Chicago lecture notes on "Variable Sets, Etendu and Variable Structures in Topoi" (of which I no longer have a copy). Peter Johnstone From cat-dist Sat Jul 18 12:19:12 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA22154 for categories-list; Sat, 18 Jul 1998 10:19:41 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <35AFA5DD.8323F00C@iswest.com> Date: Fri, 17 Jul 1998 15:28:29 -0400 From: Zhaohua Luo X-Mailer: Mozilla 4.05 [en] (Win95; I) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: abstract algebraic geometry Content-Type: multipart/alternative; boundary="------------980E00C6D8F26CAA5DFAE228" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: --------------980E00C6D8F26CAA5DFAE228 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit The following short note (see the abstract below) Uniform Functors (html) is available on Categorical Geometry Homepage at the following address: http://www.azd.com (the dvi version is under preparation) Zhaohua (Zack) Luo ------------------------------------------------------------------------------------- Uniform Functors Zhaohua Luo Abstract: In a previous note [atomic categories] we introduced the notion of an atomic category, and showed that each atomic category C carries a canonical functor to the category of sets, called the unifunctor of C. We also introduced the notion of a uniform functor between atomic categories. In this note we give an intrinsic definition of a uniform functor between any two categories with strict initials. Roughly speaking a functor is uniform if it induces isomorphisms between the complete boolean algebras of normal sieves on the objects. We show that any uniform functor to the category of sets is unique up to equivalence. A functor between Grothendieck toposes is uniform iff it induces an isomorphism between the complete boolean algebras of complemented subobjects. Since any unifunctor is uniform, this implies that a Grothendieck topos is atomic iff the complete boolean algebra of complemented subobjects of each object is atomic (or equivalently, there is a uniform functor to the category of sets). --------------980E00C6D8F26CAA5DFAE228 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit The following short note (see the abstract below)

Uniform Functors (html)

is available on Categorical Geometry Homepage at the following address:

http://www.azd.com

(the dvi version is under preparation)

Zhaohua (Zack) Luo
-------------------------------------------------------------------------------------
Uniform Functors

Zhaohua Luo

Abstract:

In a previous note [atomic categories] we introduced the notion of an atomic category, and showed that each atomic category C carries a canonical functor  to the category of sets, called the unifunctor of C. We also introduced the notion of a uniform functor between atomic categories. In this note we give an intrinsic definition of a uniform functor between any two categories with strict initials. Roughly speaking a functor is uniform if it induces isomorphisms between the complete boolean algebras of normal sieves on the objects. We show that any uniform functor to the category of sets is unique up to equivalence. A functor between Grothendieck toposes is uniform iff it induces an isomorphism between the complete boolean algebras of complemented subobjects. Since any unifunctor is uniform, this implies that a Grothendieck topos is atomic iff the complete boolean algebra of complemented subobjects of each object is atomic (or equivalently, there is a uniform functor to the category of sets).
 
  --------------980E00C6D8F26CAA5DFAE228-- From cat-dist Sat Jul 18 12:33:06 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA20645 for categories-list; Sat, 18 Jul 1998 10:18:32 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 17 Jul 1998 19:16:20 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: duality question: alg. topology Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: To all experts in algebraic topology: Is the duality I describe below known? It does not appear to be Poincare duality since there is no separate treatment of the torsion and torsion free parts. Let S be a simplicial complex, that is a set of faces of an N simplex closed under face operations. For what I am about to say, it is necessary that the empty face in dimension -1 be included so that the (co-)homology will be reduced. This means, for example, that there is a distinction between the empty simplicial complex (which has no homology) and the simplicial complex consisting of only the empty set (which has one cyclic homology group in degree -1). In fact, the former is dual to the N simplex and the latter to the N sphere. Let S' be defined as the set of complements of the complement of S. That is, for each simplex sigma not in S, the complementary simplex, whose vertices are those not in sigma, belongs to S' (and nothing else). Then for i = -1,...,N, the ith homology of S is the N-i-1st cohomology of S'. The algebraic topology books I have looked at do not mention Poincare duality, except for Lefschetz, written in 1940, and he uses a complex different from S'; in fact just opposite poset to S, since he is doing things in the generality of an arbitrary poset equipped with "incidence numbers" that are used in defining the boundary operator. In particular, his dual has the same number of elements as S, rather than 2^{N+1} - that number. One thing I find curious is that although this gives, essentially, the cohomology of S, there is no obvious way of making that into a contravariant functor. From cat-dist Fri Jul 17 14:59:04 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA13999 for categories-list; Fri, 17 Jul 1998 13:59:31 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: ct99@mat.uc.pt Message-Id: <3.0.5.32.19980717124138.007a08e0@mat.uc.pt> X-Sender: ct99@mat.uc.pt X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.5 (32) Date: Fri, 17 Jul 1998 12:41:38 +0100 To: categories@mta.ca Subject: categories: preliminary announcement Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: =================================================================== PRELIMINARY ANNOUNCEMENT =================================================================== CT99 International Category Theory Meeting Department of Mathematics University of Coimbra Coimbra, Portugal July 19-24, 1999 The Department of Mathematics of the University of Coimbra is organizing an International Meeting on Category Theory to be held at the University of Coimbra, from 19th to 24th of July, 1999. The program will consist of conferences delivered by invited speakers and contributed short talks. Scientific Committee: -------------------- Jiri Adamek (Technische Universitat Braunschweig, Germany) Bernhard Banaschewski (McMaster University, Canada) Peter T. Johnstone (University of Cambridge, UK) Andre Joyal (Universite du Quebec a Montreal, Canada) F. William Lawvere (SUNY at Buffalo, USA) Ross Street (Macquarie University, Australia) Walter Tholen (York University, Canada) Organizing Committee: -------------------- Manuela Sobral (Universidade de Coimbra) Maria Manuel Clementino (Universidade de Coimbra) Jorge Picado (Universidade de Coimbra) Lurdes Sousa (Instituto Politecnico de Viseu) Goncalo Gutierres (Universidade de Coimbra) ------------------------------------------------------------------- School on Category Theory and Applications Department of Mathematics University of Coimbra Coimbra, Portugal July 13-17, 1999 In the framework of Centro Internacional de Matematica (http://www.cim.pt) the Department of Mathematics of the University of Coimbra is also organizing a School on Category Theory and Applications from 13th to 17th of July, 1999. This school will consist of the following intensive courses, at a postgraduate level: n-Categories by John Baez (University of California, USA) Algebraic Theories by M. Cristina Pedicchio (University of Trieste, Italy) Chu Spaces: duality as a common foundation for computation and mathematics by Vaughan Pratt (Stanford University, USA). ------------------------------------------------------------------- A detailed announcement of both events will be made in October. ------------------------------------------------------------------- For further information mailto:ct99@mat.uc.pt From cat-dist Sat Jul 18 14:13:24 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA23090 for categories-list; Sat, 18 Jul 1998 13:26:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from uts.univ.trieste.it (pedicchi@uts.univ.trieste.it [140.105.48.16]) by mailserv.mta.ca (8.8.8/8.8.8) with ESMTP id NAA28934 for ; Fri, 17 Jul 1998 13:58:59 -0300 (ADT) X-Received: from localhost (pedicchi@localhost) by uts.univ.trieste.it (8.8.8/8.8.8) with SMTP id SAA22533; Fri, 17 Jul 1998 18:58:49 +0200 (MET DST) Date: Fri, 17 Jul 1998 18:58:49 +0200 (MET DST) From: "Pedicchio M. Cristina" To: Bob Rosebrugh Subject: categories: PSSL - Trieste - November 27-28 In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Peripatetic Seminar on Sheaves and Logic November 27- 28, 1998 TRIESTE - ITALY I am planning to organize a PSSL in Trieste the week-end of the 27-28 of November.Detailed informations will be send in September. Plese, feel free to contact me if you have any question. Looking forward to seeing you in Trieste, M.Cristina Pedicchio Dipartimento di Matematica Universita' di Trieste 34100 Trieste - Italy fax 39 40 6763256 tel 39 40 6763270 pedicchi@univ.trieste.it From cat-dist Sat Jul 18 19:43:05 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id SAA26019 for categories-list; Sat, 18 Jul 1998 18:26:53 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Sat, 18 Jul 1998 15:42:04 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: More algebraic topology Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I have a real question now. Suppose S is a simplicial complex of dimension n with the property that every n-1 face of every n simplex is a face of at least two n simplexes. I want to conclude that H_n(S) is non-zero. Assume that the union of the n simplexes is connected (any connected component would inherit the hypothesis). Then it seems clear geometrically that the union of the faces would enclose one or more holes, but I don't see how to actually prove this. The space would appear to have no boundary, but it also is not a manifold since a point in one of the faces could have a branched neighborhood. From cat-dist Sun Jul 19 00:27:59 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id XAA17312 for categories-list; Sat, 18 Jul 1998 23:18:24 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 18 Jul 1998 21:32:59 -0400 (EDT) From: John R Isbell To: Michael Barr cc: Categories list Subject: categories: Re: More algebraic topology In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear Mike, You are asking for every strongly connected (finite) n-complex to have nonzero $H_n$, which I think you can find -- if your Russian suffices -- in P. S. Alexandrov Combinatorial Topology, OGIZ, 1947 (660 pp.) [MR 10, 55b]. It should be around Chapter 14 or 15. I have never tried to go that far in the book, nor to read the Russian at all. I have long owned, and have used as texts in classes, the English translations which go to Chapter 12 I think; Graylock, Rochester, vol. 1, 1956 [MR 17, 882a] and vol. 2, 1957 [MR 19, 759a]. With any luck you will strike an algebraic topologist who can give you an English reference. Yours, John From cat-dist Mon Jul 20 15:13:54 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA28105 for categories-list; Mon, 20 Jul 1998 14:20:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: sjv@pop.doc.ic.ac.uk Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Mon, 20 Jul 1998 16:09:15 +0000 To: Categories From: s.vickers@doc.ic.ac.uk (Steven Vickers) Subject: categories: Alfred Sober - some recollections Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Recent mention of sober spaces brought to mind memories of Alfred Philpott Sober, whose sad death from liver failure five years ago ended a long career in topology. Though largely unpublished, it was his work that underlay the notion of what are now known as sober spaces. In Sober's view, points of topological spaces are essentially blurred and hazy: however hard you try to focus on them they always seem to jiggle about a bit - to him "focusing on a point" meant to find it within some _open_ neighbourhood, and these almost always left some room for manoeuvre. He understood the points to be exactly their open neighbourhood filters, and the spaces that would now be called non-sober were trying to impose an over-clear view of reality, making artificial distinctions between what was actually the same thing or trying to deny the existence of something he could see with his own eyes. On the related subject of continuity, he saw its essence as that of a function was that was not unduly upset by this jiggling: as long as the argument didn't jiggle too much, the result wouldn't either, and he liked to demonstrate the idea by carrying a tray of drinks across a crowded room. Though not one of the founders of locale theory, he was aware of the idea and greatly sympathetic to it - though he couldn't see any reason for using the French spelling and pronunciation. Once when in the midst of explaining his ideas the lattice structures started to become manifest and he would excitedly talk about "getting down to the local". He studied initially at Cambridge under the influence of Charles Wells (the Bedford Charles Wells, NOT the well-known category theorist) and his thesis, starting off on Klein bottles, soon took in Gross bottles too. He made his academic home in the University of Portsmouth and was much loved by both his colleagues and his students for his parties and for his never-failing warm welcome "Come in and what'll you have?" He is much missed by all who knew him. Steve Vickers. From cat-dist Mon Jul 20 15:14:10 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA27346 for categories-list; Mon, 20 Jul 1998 14:16:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 20 Jul 1998 07:44:05 -0400 (EDT) From: Peter Freyd Message-Id: <199807201144.HAA17291@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: 2 Barr questions Cc: barr@math.mcgill.ca Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I've got well over a thousand e-mails waiting to be looked at. I'm working on the pile from both ends. Two recent postings from Mike Barr: 1) The duality he describes sounds like Spanier-Whitehead duality. It's usually defined geometrically. Embed a finite complex into a higher-dimensional sphere, take the complement, contract it to a finite complex. Do this in the stable-homotopy category (obtained by forcing the suspension functor on the homotopy category to become an automorphism) and normalize the dimensions so that the dual of a space has the negative of its dimension. Show that the embeddings can be chosen in a coherent fashion to obtain a self-duality for stable homotopy. (The last step is non-trivial and the only person I know who verified it is Frank Adams, and that wasn't published. Does anyone have a citation?) 2) If every n-1 cell of an n-dimensional finite complex is the face of _exactly_ 2 n-dimensional cells then there's a fairly easy argument that the n-dimensional Z_2 cohomology is non-trivial. But if the condition is changed to "_at least_ 2 n-dimensional cells" then the space can be contractible. Start with the closed unit disk in the complex plane and glue the boundary onto the closed unit interval (which constitutes half of the intersection of the disk and the real line) by identifying a point x on the interval with e^(2(pi)xi) on the boundary. If one triangulates this space, each edge will be a face of either 2 or 3 triangles. One way of seeing that this is contractible is to consider first the space obtained by identifying just the upper half of the boundary with the unit interval by identifying a point x on the interval with e^((pi)xi) on the boundary. Recalling that the homotopy type of a space is unchanged when reasonable closed contractible subsets are collapsed to points, note that if the lower half of the boundary is collapsed to a point we obtain the first space. On the other hand, the upper half (together with the unit interval) is contractible, and when it's collapsed to a point we obtain the unit disk. By taking the suspension of this example we can get an example in every larger finite dimension. This example is a mapping cone. Take the map from the circle to the circle that wraps the first third of the circle around the circle, wraps the second third around in the opposite direction, and the last third in the original direction. This map is, of course, homotopic to the identity map. The mapping-cone construction depends only on the homotopy type of the map. The mapping cone of the identity map on the circle is, of course, the disk. From cat-dist Mon Jul 20 15:14:39 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA30459 for categories-list; Mon, 20 Jul 1998 14:13:03 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 20 Jul 1998 13:27:15 +1200 (NZST) From: Paul Bonnington Message-Id: <199807200127.NAA06960@aitken.scitec.auckland.ac.nz> To: categories@mta.ca Subject: categories: DMTCS99+CATS99 final call Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: FINAL CALL FOR PAPERS (Please Circulate) DMTCS'99, Discrete Mathematics and Theoretical Computer Science and CATS'99, Computing: The Australasian Theory Symposium University of Auckland and CDMTCS, Auckland, New Zealand 18-21 January 1999 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DMTCS'99 and CATS'99 will be part of the Australsian Computer Science Week (ACSW'99). Original papers are solicited in all areas of discrete mathematics and theoretical computer science. Typical, but not exclusive, topics of interest include: (a) abstract data types and specifications, (b) algorithms and data structures, (c) automata and formal languages, (d) computability and complexity, (e) computational algebra, biology, geometry, logic and number theory, (f) concurrency, distributed systems and parallel computing, (g) constructive mathematics, (h) discrete mathematics, combinatorial computing and category theory, (i) formal semantics, specification, synthesis and verification, (j) hybrid systems and nonmonotonic logic. Authors are invited to submit papers either in hard copy by post, or electronically by email, to the address below. Electronic submissions should be in PostScript format, printable in a standard Unix environment. LaTeX source of final versions of accepted papers will be required. Submissions should not exceed 15 pages and include an e-mail address of the corresponding author. Joint submissions to other conferences are not permitted. At least one author of each accepted paper is expected to register by Nov. 6th and present their work at the conference. The proceedings will be published by Springer-Verlag, Singapore in the DMTCS Series, and will be made available during the conference. Invited Speakers: R. Downey (UVW, NZ) J. Goguen (UCSD, USA) A. Nerode (Cornell, USA) J. Pach (Hungarian Academy of Sciences) A. Restivo (U. Palermo, Italy) G. Walsh (U. Ottawa) Address For Submissions: DMTCS'99+CATS'99 (Attn: Michael Dinneen), Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand, Email: mjd@cs.auckland.ac.nz Cost of Participation: The registration fee is A $400 (which includes the dinner, excursion and proceedings), or A $100 for students (including only the proceedings). For More Information: See the home-page of the conference http://www.tcs.auckland.ac.nz/~acsw99/, or contact the local chair Bakh Khoussainov at bmk@cs.auckland.ac.nz. --------------------------------------------------------------------------- Conference Committee: C.P. Bonnington C.S. Calude (general chair) E. Calude R. Coles, P.B. Gibbons U. Guenther B. Khoussainov (local chair) ACSW'99 Contact Members: R.W. Doran (general chair) P. Fenwick Programme Committee: R.J. Back, TUCS, Finland M. Conder, U. Auckland, NZ B. Cooper, U. Leeds, UK M.J. Dinneen, U. Auckland, NZ (chair) R. Goldblatt, Victoria U., NZ S. Goncharov, Novosibirsk U., Russia J. Harland, RMIT, Australia R.E. Hiromoto, UTSA, USA H. Ishihara, JAIST, Japan M. Ito, Kyoto S.U., Japan M. Li, U. Waterloo, Canada X. Lin, UNSW, Australia R. Shore, Cornell U., USA T. Tokuyama, IBM, Japan D. Wolfram, ANU, Australia Proceedings Editors: C.S. Calude and M.J. Dinneen --------------------------------------------------------------------------- Important Dates: Submissions Due: 31 July 1998 Notification Date: 09 Oct. 1998 Final Copies Due: 30 Oct. 1998 Registration Date (for authors): 06 Nov. 1998 (for others): January 1999 --------------------------------------------------------------------------- %%% DMTCS'99+CATS'99 Call for Papers %%% %%% Disclaimer: The following is very hacked LaTeX. %%% \documentstyle[11pt]{article} \pagestyle{empty} \oddsidemargin=-18.5truept \textwidth=7in %\topmargin=0.12in \topmargin=-0.4in \textheight=9.7in \newcommand{\mylistlabel}{\hspace\labelsep } \newenvironment{mylist}{\begin{list}{\hbox{}}% {\leftmargin 18pt \labelwidth 0pt \itemindent-\leftmargin \itemsep -1pt \let\makelabel\mylistlabel}}% {\end{list}} \newcommand{\fillin}{\typeout{*** Fill in! ***}??} \newcommand{\recheck}[1]{\typeout{*** Recheck This! ***}#1} \begin{document} %%% %%% CDMTCS Logo %%% % % \hbox{}\vspace*{-0.8in}\hfill\makebox[5pt]{\epsffile{ieee-cs.eps}} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{-1.2in} \begin{center} % \makebox[5pt]{\epsffile{ieee-cs.eps}} \\[3ex] \LARGE\bf Call for Papers\\[2ex] \Large\bf \mbox{DMTCS'99---Discrete Mathematics and Theoretical Computer Science}\\[0pt] \Large and\\[0pt] \Large\bf CATS'99---Computing: The Australasian Theory Symposium\\[3ex] {\large University of Auckland and CDMTCS, Auckland, New Zealand \\[2ex] \large\bf 18-21 January 1999} \end{center} \vspace*{4ex} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% %%% Sidebar %%% \begin{minipage}[t]{2.0in}\footnotesize \medskip %\noindent{\bf University of Auckland}\\ \noindent{\bf Conference Committee} \begin{mylist}\raggedright \item C.P. Bonnington % (information) \item C.S. Calude (general chair) \item E. Calude % (venue) \item R. Coles % (records) \item P.B. Gibbons % (accomodation) \item U. Guenther % (registration) \item B. Khoussainov (local chair) \end{mylist} \medskip \noindent{\bf ACSW'99 Contact Members} \begin{mylist}\raggedright \item R.W. Doran (general chair) \item P. Fenwick \end{mylist} \medskip \noindent{\bf Programme Committee} \begin{mylist}\raggedright \item R.J. Back, TUCS, Finland \item M. Conder, U. Auckland, NZ \item B. Cooper, U. Leeds, UK \item M.J. Dinneen, U. Auckland, NZ (chair) \item R. Goldblatt, Victoria U., NZ \item S. Goncharov, Novosibirsk U., Russia \item J. Harland, RMIT, Australia \item R.E. Hiromoto, UTSA, USA \item H. Ishihara, JAIST, Japan \item M. Ito, Kyoto S.U., Japan \item M. Li, U. Waterloo, Canada \item X. Lin, UNSW, Australia \item R. Shore, Cornell U., USA \item T. Tokuyama, IBM, Japan \item D. Wolfram, ANU, Australia \end{mylist} \medskip \noindent{\bf Proceedings Editors} \begin{mylist}\raggedright \item C.S. Calude \item M.J. Dinneen \end{mylist} \medskip\noindent{\bf Important Dates} \begin{mylist}\raggedright\frenchspacing \item \makebox[1.1in][l]{Submissions Due:} \makebox[0.26in][l]{31 July 1998} \item \makebox[1.1in][l]{Notification Date:} \makebox[0.26in][l]{9 Oct. 1998} \item \makebox[1.1in][l]{Final Copies Due:} \makebox[0.26in][l]{30 Oct. 1998} \item \makebox[1.1in][l]{Registration Date} \item \makebox[1.1in][l]{for Authors:} \makebox[0.26in][l]{6 Nov. 1998} \end{mylist} \end{minipage} %%% %%% Vertical Line %%% \hspace*{4.75pt}\rule[-7.7in]{0.5pt}{7.9in}\hspace*{4.75pt} %%% %%% Main Column %%% \begin{minipage}[t]{4.25in} \parskip\smallskipamount DMTCS'99 and CATS'99 will be part of the Australsian Computer Science Week (ACSW'99). Original papers are solicited in {\sl all\/} areas of discrete mathematics and theoretical computer science. Typical, but not exclusive, topics of interest include: (a) abstract data types and specifications, (b) algorithms and data structures, (c) automata and formal languages, (d) computability and complexity, (e) computational algebra, biology, geometry, logic and number theory, (f) concurrency, distributed systems and parallel computing, (g) constructive mathematics, (h) discrete mathematics, combinatorial computing and category theory, (i) formal semantics, specification, synthesis and verification, (j) hybrid systems and nonmonotonic logic. Authors are invited to submit papers either in hard copy by post, or electronically by email, to the address below. Electronic submissions should be in PostScript format, printable in a standard Unix environment. \LaTeX{} source of final versions of accepted papers will be required. Submissions should not exceed 15 pages and include an e-mail address of the corresponding author. Joint submissions to other conferences are {\sl not\/} permitted. At least one author of each accepted paper is expected to register by Nov.~6th and present their work at the conference. The proceedings will be published by Springer-Verlag, Singapore in the DMTCS Series, and will be made available during the conference. \medskip {\bf Invited Speakers:} R.~Downey (UVW, NZ), J.~Goguen (UCSD, USA), A.~Nerode (Cornell, USA), J.~Pach (Hungarian Academy of Sciences) and A.~Restivo (U. Palermo, Italy). \medskip {\bf Address For Submissions:} DMTCS'99+CATS'99 (Attn: Michael Dinneen), Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand, {\tt mjd@cs.auckland.ac.nz}. \medskip {\bf Cost of Participation:} The registration fee is A\$400 (which includes the dinner, excursion and proceedings), or A\$100 for students (including only the proceedings). \medskip {\bf For More Information:} See the home-page of the conference \verb|http://www.tcs.auckland.ac.nz/~acsw99/|, or contact the local chair Bakh Khoussainov at {\tt bmk@cs.auckland.ac.nz}. \end{minipage} \end{document} From cat-dist Mon Jul 20 15:15:43 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA30328 for categories-list; Mon, 20 Jul 1998 14:21:53 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Mon, 20 Jul 1998 13:20:01 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Answers Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: I got the same counter-example from Peter Johnstone and Peter Freyd. PJ called it the dunce cap and described it as a triangle with the three edges identified, one in the reverse direction. PF described it in a more complicated way that made it easier to see it actually contractible. And the latter was really what I wanted to refute. When I saw PJ's example, I mistakenly thought it still had a 1-cycle. The smallest triangulation I found had 8 vertices, which is still too large to compute by hand with. The dual complex still has over 200 simplexes and that is just too many. If anyone knows a smaller triangulation, I would like to know it. Thanks to all who responded. Michael From cat-dist Wed Jul 22 15:09:28 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA10194 for categories-list; Wed, 22 Jul 1998 13:41:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 21 Jul 1998 13:55:47 -0400 (EDT) From: Susan Niefield To: categories@mta.ca Subject: categories: revised preprint available In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: A revised version of the following reprint is available at http://www1.union.edu/~niefiels/ESU.ps http://www1.union.edu/~niefiels/ESU.dvi EXPONENTIABILITY AND SINGLE UNIVERSES by Marta BUNGE and Susan NIEFIELD ABSTRACT - In this paper, we first consider known universes for pairs of opposite notions such as those of discrete fibrations/discrete opfibrations and of open/closed locale inclusions, and then extrapolate these in order to introduce new single universes for open/closed inclusions of subcategories and for functions/distributions on a topos. A key factor that these notions have in common is exponentiability in the ambient category. Along the way, we (1) prove that, for a factorization linearly ordered small category B, the category of discrete Giraud-Conduche fibrations over B is a (model generated) topos, (2) characterize locally closed inclusions in the category Cat of small categories, (3) investigate ``generalized coverings'' in topos theory, including branched coverings, cuts, and complete spreads, and (4) examine the preservations of exponetiability under the passage from Cat/B to the category of Grothendieck toposes over the presheaves PB. From cat-dist Wed Jul 22 15:12:54 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA32174 for categories-list; Wed, 22 Jul 1998 13:40:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <35B4D3D4.E4085B42@doc.ic.ac.uk> Date: Tue, 21 Jul 1998 18:45:56 +0100 From: Susan Eisenbach X-Mailer: Mozilla 4.05 [en] (WinNT; I) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: java Workshop Reminder Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: About two months ago I announced a workshop on formal underpinnings of Java. Since then I've had email from Java Software at Sun (what used to be called Javasoft) expressing interest. They said: Our main interest is in formal specification of Java byte code verification because that is an area where a formal spec is both realistic and sorely needed. We hope to be able to adapt some approach developed in the research community. If you are doing work in this or related work there is still time to submit an extended abstract to our workshop. Formal Underpinnings of Java - an OOPSLA'98 Workshop Important Dates Submissions: 31 July 1998 Notifications: 20 August 1998 Final Versions: 20 September 1998 Workshop: Sunday, 18 October 1998, Vancouver, Canada Java offers a novel paradigm for program deployment. It supports intermediate code that is dynamically loaded from remote sites - sometimes without the user's knowledge. For Web pages, Java applets can greatly improve interactivity; for Java developers, the Java paradigm promises benefits in portability and manageability. However, the Java paradigm also opens new possibilities for abuse and has caused concern about security. The application of formal methods to the Java paradigm aims to provide a better understanding of the approach by rigorously formulating and trying to prove the soundness of binary compatibility, type safety, security and other guarantees made by Java. It also aims to provide some guidance for further development of the paradigm by uncovering possible design flaws and by supplying a platform for the description of future extensions. This workshop aims to bring together researchers to share new ideas and results. Since the main focus in selecting workshop contributions will be the intrinsic interest and timeliness of the work, authors are encouraged to submit (polished) descriptions of work in progress as well as papers describing completed projects. The proceedings will be published as a Princeton University technical report and be available from the web. We solicit submissions on original research on the following, or related subjects: semantics of Java semantics of byte code, correctness of the byte code verifier formal verification of Java programs separate compilation, binary compatibility dynamic linking and loading security policy practicality of formal methods for Java comparison of approaches, tools Electronic versions of extended abstracts between 2500 and5000 words (approximately 5-10 pages) should be e-mailed to S.Eisenbach@doc.ic.ac.uk by Friday, 31 July 1998, using US-letter or A4 size,Postscript or PDF. The submission may be included inline in the message or as a MIME attachment only. (If electronic submission is impossible, postal submissions must be received by Friday 31 July 1998; enclose 4 double-sided copies, a return postal address, a phone number, and a return e-mail address.) Receipt of the submissions will be acknowledged by e-mail. The authors should inquire in case a prompt acknowledgment is not received. Program Committee Susan Eisenbach, Imperial College Jim Alves-Foss, University of Idaho Drew Dean, Princeton University Sophia Drossopoulou, Imperial College Tobias Nipkow, Technische Universität München Raymie Stata, Digital Equipment Corporation Correspondence and questions should be sent to S.Eisenbach@doc.ic.ac.uk http://www-dse.doc.ic.ac.uk/~sue/oopsla/cfp.html From cat-dist Wed Jul 22 18:20:10 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA12464 for categories-list; Wed, 22 Jul 1998 16:58:34 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 22 Jul 1998 14:27:35 +0200 (MET DST) From: Dines Bjorner Message-Id: <199807221227.OAA27140@solaris1.it.dtu.dk> To: categories@mta.ca Subject: categories: FM'99 World Congress on Formal methods, 20-24 Sept. 1999, Toulouse, France Cc: Nico.Plat@acm.org, db@toga.it.dtu.dk Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-MD5: r83f286kpUsVcaN5t8Wx9Q== Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear Colleague, ACM, AMAST, ASM, EATCS, ETAPS, EU, FME, IFIP, IEEE CS, IPSJ, JSSST are co-sponsoring and FME is organising: FM'99: World Congress on Formal Methods (in the development of computing systems) 20-24 Sept. 1999, Intl.Congress Ctr., Toulouse, France You may wish to inspect: FM'99 Main http://www.it.dtu.dk/~db/fm99/FM99Main/FM99Main.html and/or FM'99 Congress http://www.it.dtu.dk/~db/fm99/FM99Congress/FM99Congress.html from where documents on separate Congress events can be accessed: Technical Symposium http://www.it.dtu.dk/~db/fm99/FM99Symposium/FM99Symposium.html including: Mini-Tracks http://www.it.dtu.dk/~db/fm99/FM99Minis/FM99Minis.html Tools Fair & Applications Forum http://www.it.dtu.dk/~db/fm99/FM99Tools/FM99Tools.html Users and Working Group Meetings http://www.it.dtu.dk/~db/fm99/FM99UsersGroups/FM99UsersGroups.html FM'99 Industry Tutorials http://www.it.dtu.dk/~db/fm99/FM99Tutorials/FM99Tutorials.html Sincerely Dines Bjorner General Chair From cat-dist Wed Jul 29 09:36:27 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id HAA01736 for categories-list; Wed, 29 Jul 1998 07:44:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Klaus Keimel Message-Id: <199807251457.AA044378669@fb0432.mathematik.tu-darmstadt.de> Subject: categories: Visiting Position To: selinger@harald.daimi.aau.dk, amast@cs.utwente.nl, bra-types@cs.chalmers.se, categories@mta.ca, concurrency@cwi.nl, cphc-jobs@mailbase.ac.uk, eacsl@dimi.uniud.it, eatcs-it@cs.unibo.it, facs@lboro.ac.uk, logic@CS.Cornell.EDU, mfpsmail@math.tulane.edu, THEORY-A@LISTSERV.NODAK.EDU, types@cs.indiana.edu Date: Sat, 25 Jul 1998 16:57:49 MESZ X-Mailer: Elm [revision: 109.19] Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Visiting Lecturer/Professor in Computer Science There is a Visiting Lectureship/Professorship available at the University of Technology at Darmstadt for a period of either six months or one year starting on October 1, 1998. (There is an unexpected vacancy that occurred just yesterday.) In October we are starting a new curriculum 'Mathematics with Computer Science' with an international orientation. In the first year, courses are taught in English. There will be German and international students. The visiting Lecturer/Professor is expected to teach the first year course of Computer Science in ENGLISH within this framework. The remuneration will be according to the German system depending on qualification and age. If you are interested, please contact Prof. Dr. Klaus Keimel Fachbereich Mathematik Technische Universitaet D-64289 Darmstadt, Germany Tel. + 49 6151 162215 Fax. + 49 6151 164011 e-mail: keimel@mathematik.tu-darmstadt.de Please pass this announcement to any person that could be interested. More information about the new course: http://www.mathematik.tu-darmstadt.de/dekan/MCS/mcs-detailed.html From cat-dist Fri Jul 31 09:39:43 1998 Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA21681 for categories-list; Fri, 31 Jul 1998 08:17:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Edmund Robinson Message-Id: <199807301432.PAA12050@wax.dcs.qmw.ac.uk> Subject: categories: Lectureships at Queen Mary and Westfield To: categories@mta.ca, concurrency@cwi.nl, types@cs.indiana.edu, mfpsmail@math.tulane.edu Date: Thu, 30 Jul 1998 15:32:50 +0100 (BST) X-Mailer: ELM [version 2.4 PL25] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Please accept my apologies if (more accurately when) you receive multiple copies of this message. Since it is summer, please also consider informal discussions with me as acting Head of Department (edmundr@dcs.qmw.ac.uk). best wishes Edmund Robinson ------------------------------------------------------- Queen Mary and Westfield College, London, UK Lecturer(s) in Computer Science Following recent successful appointments the Department of Computer Science is seeking further Lecturers. The Department is consolidating its research strength and seeking to appoint strong researchers in the areas of Distributed Systems, Human Computer Interaction, Computer Vision or Programming Languages and Theoretical Computer Science. Applicants with research interests in mobile computing, multimedia and CSCW are encouraged. At least one of the posts will be targeted at the areas of Distributed Systems or Human Computer Interaction. Candidates should be able to teach a range of undergraduate and postgraduate Computer Science courses. Salary according to experience range from Lecturer A/B UKP 18,500 to UKP 30,679 p.a. inclusive, rising to UKP 18,789 - UKP 31,182 (UK pounds) from 1 October 98. Informal enquiries may be made to Professor Heather Liddell (Head of Department) on 0171 975 5167 - email: heather@dcs.qmw.ac.uk or Professor Peter Johnson on 0171 975 5224 - email: pete@dcs.qmw.ac.uk. Further details of the Department, its research activity, and the expected role of the appointees are available on-line. For a printed copy of these details and an application form please telephone our 24 hour Recruitment Line on 0171 975 5171 or Email: coll-recruit@qmw.ac.uk quoting Reference 98125LC. Completed application forms should be returned by 18th August 1998 to the Personnel Office, Queen Mary and Westfield College, London E1 4NS.