From rrosebru@mta.ca Wed Sep 6 20:05:13 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA07440 for categories-list; Wed, 6 Sep 2000 19:03:08 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 6 Sep 2000 13:43:13 -0400 (EDT) From: Peter Freyd Message-Id: <200009061743.e86HhCQ25057@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Barr question Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 1 Mike Barr asked: Suppose X is an abelian category and T:X --> Ab is a left- exact functor. Say an object E is T-effaceable if for every exact sequence 0 --> E --> B --> A --> 0, the induced TB --> TA is surjective. Now suppose that 0 --> E' --> E --> E'' --> 0 is an exact sequence in which E and E' are T-effaceable. Does it follow that E'' is? (Well, actually he asked the dual question. But they're equivalent.) The answer is no. Suppose we have an abelian category with a map x:E --> E where 1) E is injective; 2) the image of x is not injective; and 3) x is not a zero-divisor in the ring of endomorphisms of E. Let E' denote the kernel of x, E'' the image and F the cokernel. Let T be the representable functor (F,-). In order of difficulty: E is T-effaceable because being condition 1 says that it's T-effaceable for any old T. E'' is not T-effaceable because if the exact sequence 0 --> E'' --> E --> F --> 0 were to be carried into an exact sequence 0 --> (F,E'') --> (F,E) --> (F,F) --> 0 then the identity element in (F,F) would have a pre-image and the 0 --> E'' --> E --> F --> 0 would split, forcing E'' to be injective (violating condition 2). E' is T-effaceable because given 0 --> E' --> B --> A --> 0 exact we show that 0 --> (F,E') --> (F,B) --> (F,A) --> 0 exact by showing that any F --> A has a pre-image in (F,B); we do that by first constructing the exact diagram (add your own downwards arrowheads): 0 --> E'--> C --> F --> 0 1| | | 0 --> E'--> B --> A --> 0 by taking the right-hand square as a pullback; we need to show that the top sequence splits; construct: 0 --> E'--> C --> F --> 0 1| | | 0 --> E'--> E --> E''--> 0 by using the injectivity of E to obtain the middle vertical and the exactness of the rows to obtain the right-hand vertical; note x that E --> E --> F --> E'' --> E is necessarily the zero-map, hence E --> F --> E'' --> E is a zero-divisor for x, and condition 3 together with the epiness of E --> F and the mononess of E'' -> E forces F --> E'' to be the zero-map; that forces C --> E --> E'' to be the zero-map; and that says that C --> E can be factored through E' --> E; but that implies that E' --> C is a split mono; so C --> F is a split epi. How do we know that the three numbered conditions can be met? There must be an easier way, but the one that occurs to me is to use the category Joel Cohen named in his book the Freyd Category (named not after me, he says, but my daughter). It's the abelian category in which the stable-homotopy category of finite complexes appears as the full subcategory of injective-projectives. Take E to be the sphere. Its ring of endomorphisms is the ring of integers and we can take x = 2. Using that the endomorphisms form a connected ring (no non-trivial idempotents) we know that x is not epi (else it would be a split epi) and its image, being a proper non-trivial subobject, can't be injective. (If you try for a dual example by replacing "injective" with "projective", avoid the temptation of taking E to be free -- can't work.) When Mike and I started, category theory was classified (by MR and just about everybody) as homological algebra. Mike was right, in fact, when he said, "I thought this would be a simple application of the snake lemma", albeit in the other direction. Assuming that T could be taken as a functor of the form (F,-) a little homological algebra says that what's needed is an object E' where Ext(F,E') is trivial but Ext^2(F,E') is not. I thought it might be best -- since category theory is no longer a subset of homological algebra -- to get rid of the Exts. From rrosebru@mta.ca Sat Sep 9 13:51:43 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA32402 for categories-list; Sat, 9 Sep 2000 12:52:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 Message-Id: Date: Thu, 7 Sep 2000 17:23:13 +0100 To: etaps2001@disi.unige.it From: Etaps 2001 Subject: categories: ETAPS 2001: SECOND ANNOUNCEMENT & CALL FOR SUBMISSIONS Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 2 ETAPS 2001 APRIL 2 - 6, 2001 - GENOVA, ITALY The European Joint Conferences on Theory and Practice of Software (ETAPS) is a loose and open confederation of conferences and other events that has become the primary European forum for academic and industrial researchers working on topics relating to Software Science. http://www.disi.unige.it/etaps2001/ SECOND ANNOUNCEMENT & CALL FOR SUBMISSIONS ----------------------------------------------------------------------- 5 Conferences - Tutorials - Tool Demonstrations - 8 Satellite Events ----------------------------------------------------------------------- CONFERENCES ----------------------------------------------------------------------- CC 2001: International Conference on Compiler Construction Chair: Reinhard Wilhelm ESOP 2001, European Symposium On Programming Chair: David Sands FASE 2001, Fundamental Approaches to Software Engineering Chair: Heinrich Hussmann FOSSACS 2001, Foundations of Software Science and Computation Structures Chair: Furio Honsell TACAS 2001, Tools and Algorithms for the Construction and Analysis of Systems Chairs: Tiziana Margaria and Wang Yi Prospective authors are invited to submit, before October 20, 2001, full papers in English presenting original research. Submitted papers must be unpublished and not submitted for publication elsewhere. In particular, simultaneous submission of the same contribution to multiple ETAPS conferences is forbidden. The proceedings of each main conference will be published as a separate volume in the Springer Verlag Lecture Notes in Computer Science series. TUTORIALS ----------------------------------------------------------------------- Proposals for half-day or full-day tutorials related to ETAPS 2001 are invited. Tutorial proposals will be evaluated on the basis of their assessed benefit for prospective participants to ETAPS 2001. Contact: Bernhard Rumpe (Technische Universitaet Munchen, Germany) TOOL DEMONSTRATIONS ----------------------------------------------------------------------- Demonstrations of tools presenting advances on the state of the art are invited. Submissions in this category should present tools having a clear connection to one of the main ETAPS conferences, possibly complementing a paper submitted separately. These should not be confused with contributions to TACAS, which emphasizes principles of tool design, implementation, and use, rather than focusing on specific domains of application. Contact: Don Sannella (University of Edinburgh) SATELLITE EVENTS ----------------------------------------------------------------------- Besides the five main conferences the following satellite events are planned for ETAPS 2001 CMCS: Co-algebraic Methods in Computer Science Contact: Ugo Montanari (Universita' di Pisa, Italy) ETI Day: Electronic Tool Integration platform Day Contacts: Tiziana Margaria (Universitaet Dortmund, Germany) and Andreas Podelski (MPI Saarbrucken, Germany) JOSES: Java Optimization Strategies for Embedded Systems Contact: Uwe Assmann (Universitat Karlsruhe, Germany) LDTA: Workshop on Language Descriptions, Tools and Applications Contact: Mark van den Brand (CWI Amsterdam, The Netherlands) PFM: Proofs For Mobility Contact: Davide Sangiorgi (INRIA-Sophia Antipolis, France) RelMiS: Relational Methods in Software Contact: Wolfram Kahl (Universitaet der Bundeswehr Munchen, Germany) UNIGRA: Uniform Approaches to Graphical Process Specification Techniques Contact: Julia Padberg (Technische Universitaet Berlin, Germany) WADT: Workshop on Algebraic Development Techniques Contact: Maura Cerioli (DISI-Universita' di Genova, Italy) IMPORTANT DATES: ----------------------------------------------------------------------- October 20, 2000: Submissions Deadline for the Main Conferences, Demos and Tutorials December 15, 2000: Notification of Acceptance/Rejection January 15 2001: Camera-ready Version Due April 2-6, 2001: ETAPS 2001 in Genova March 31 - April 8, 2001: Satellite Events ----------------------------------------------------------------------- [ Sorry for multiple copies. Do not reply to this message. If you believe we have sent this to a list not appropriate, please let us know by mailing to etaps2001@disi.unige.it ] From rrosebru@mta.ca Mon Sep 11 12:43:17 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA24065 for categories-list; Mon, 11 Sep 2000 11:48:19 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: "Walter Tholen" Message-Id: <1000911092446.ZM162904@pascal.math.yorku.ca> Date: Mon, 11 Sep 2000 09:24:45 -0400 X-Mailer: Z-Mail (4.0.1 13Jan97) To: categories@mta.ca Subject: categories: AMS SS J1 (Applied Categorical Structures) in Toronto MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: A X-Keywords: X-UID: 3 Dear Category Theorist: This is the final announcement for the Special Session on "Applied Categorical Structures" at the up-coming AMS Meeting in Toronto, Sept. 23&24. The Session will be held in Room 2173 of the Medical Sciences Building on the downtown campus of the University of Toronto. It will start on Saturday at 9am and finish on Sunday at 5pm. For comprehensive and continually updated meeting and program information, including accommodation in Toronto, see http://www.ams.org/meetings/ For the the program of the Session, see also the end of this message. There has been one change since Andre' Joyal is not able to attend, due to sudden unavoidable circumstances. There will be a WELCOME PARTY on Friday, September 22, starting at 7pm, for participants of the Session. With funds provided by York University we are pleased to be able to invite you and your spouse/friend to a complimentary buffet dinner (open till 10pm) in the Thai restaurant "Sawaddee" at 150 Avenue Road, Toronto, tel. (416) 921 9198. The restaurant is located at the north-west corner of the intersection of Avenue Road with Davenport, which is 7 (very short) blocks north of Bloor St. It's about a 15-minute walk from the UofT-campus, and less than 5 minutes from the Howard Johnson Inn which we mentioned in our previous message. The walk from the Days Inn on Carlton St would be about 30 minutes; a reasonable alternative to walking all the way or taking a short taxi ride would be walking westbound from the hotel on Carlton and College to Bay Street and taking the "Bay" bus no.6 north and to get off right at the intersection Avenue Rd/Davenport (subway token or exact fare $2 required). If coming by car to the restaurant, your best bet would be to search for spots on the streets in the area north west of the restaurant, success not guaranteed. In order for us to know the approximate number of participants, PLEASE LET US KNOW BY FRIDAY, SEPTEMBER 15, WHETHER YOU'LL BE COMING TO THE WELCOME PARTY, by e-mailing tholen@mathstat.yorku.ca (see form below). We look forward to seeing you in Toronto. Joan Wick Pelletier Walter Tholen ******************************************************************************* I shall be attending the "Welcome Party" on Friday, September 22: YES/NO I will be accompanied by my spouse/friend: YES/NO NAME: ********************** Send to tholen@mathstat.yorku.ca ********************** PROGRAMME Saturday, Sept. 23: 9:00 Matt Brin (see abstract below) 3:00 Stephen Awodey 9:30 Myles Tierney 3:30 Lars Birkedal 10:00 Jack Duskin 4:00 David Benson 10:30 Marco Grandis 4:30 John MacDonald 11:00 Enrico Vitale 5:00 Richard Wood Sunday, Sept. 24: 9:00 Marta Bunge 2:00 Joachim Lambek 9:30 Michael Makkai 2:30 James Madden 10:00 Robin Cockett 3:00 Gloria Tashjian 10:30 M. M. Mawanda 3:30 Robert Pare 11:00 F. William Lawvere 4:00 Jiri Rosicky 4:30 F. J. O. Souza All talks are 25 minutes long. The titles follow. The full abstracts may be seen at the web site cited above. Abstract # Title Authors Date Received 957-18-265 On the pivotal, symmetric case of involutory Hopf 13-jul-2000 objects. Fernando J. O. Souza*, fernando@math.uic.edu 957-18-235 Higher category theory. 12-jul-2000 Andre Joyal*, joyal@math.uqam.ca 957-06-218 Injective hulls of partially ordered monoids. 12-jul-2000 J. Lambek* 957-18-214 Modelling a sketch in an object in a 2-category. 11-jul-2000 Michael Johnson, mike@ics.mq.edu.au Robert Rosebrugh, rrosebru@mta.ca R. J. Wood*, rjwood@mathstat.dal.ca 957-18-204 Open problems on finiteness and their counting 11-jul-2000 measures. Mbila-Mambu Mawanda*, mm.mawanda@nul.ls 957-18-199 Monoreflections in categories of ordered rings. 10-jul-2000 James J Madden*, madden@math.lsu.edu 957-18-198 Nerves of Bicategories: Morphisms and Simplicial 10-jul-2000 Maps. John W Duskin*, duskin@math.buffalo.edu 957-18-157 A summary report on the state of our knowledge of 05-jul-2000 weak higher dimensional categories. Michael Makkai*, makkai@math.mcgill.ca 957-18-140 Dominances and Spread Completions. 04-jul-2000 Marta C Bunge*, bunge@math.mcgill.ca 957-18-132 Finitely productive classes of uniform spaces 03-jul-2000 which generate cartesian-closed categories. Gloria Tashjian* 957-68-123 Certain spans of sketches model problems of 29-jun-2000 complexity NP. David B Benson*, dbenson@eecs.wsu.edu 957-18-107 Flat covers and factorizations. 27-jun-2000 Jiri Rosicky*, rosicky@math.muni.cz 957-18-90 Free Double Categories and the Word Problem for 25-jun-2000 Groups. Robert Par\'e*, pare@mscs.dal.ca Robert MacG. Dawson, rdawson@husky1.stmarys.ca 957-18-77 A higher dimensional homotopy sequence. 22-jun-2000 Marco Grandis, grandis@dima.unige.it Enrico Vitale*, vitale@agel.ucl.ac.be 957-18-76 Some absolute pullbacks and pushouts in 22-jun-2000 $\boldsymbol{\Delta}$. Myles Tierney*, tierney@math.rutgers.edu 957-18-61 Monads and Structure. 16-jun-2000 John L. MacDonald*, johnm@math.ubc.ca 957-18-59 Relating realizability using sheaves. 16-jun-2000 Steve Awodey*, awodey@cmu.edu Andrej Bauer Dana S Scott 957-03-51 Relative and Modified Relative Realizability. 13-jun-2000 Lars Birkedal*, birkedal@itu.dk Jaap van Oosten, jvoosten@math.uu.nl 957-18-39 Higher fundamental functors in some categories of 07-jun-2000 presheaves. Marco Grandis*, grandis@dima.unige.it 957-18-30 Game theory revisited: categorical proof theories 31-may-2000 for games. J. Robin B. Cockett*, robin@cpsc.ucalgary.ca 957-18-19 Toposes and Continuum Microphysics. 22-may-2000 F. William Lawvere*, wlawvere@acsu.buffalo. NEW The chameleon groups of Richard J. Thompson: 09-sep-2000 categories with multiplication. Matt Brin*, matt@math.binghamton.edu. > ----------------------------------------------------------------------------- > Matt Brin: The chameleon groups of Richard J. Thompson: categories with > mutliplication > > Abstract: > > We show that any category with a functoral multiplication has > asociated to it a handful of groups that are strongly related to > infinte, finitely presented groups discovered by Richard Thompson. > To add weight to the connection between the multiplication and the > groups, we prove that if associativity and commutativity > equivalences are given, then they are are coherent (in the sense of > MacLane) if and only if two of the groups turn out to be isomorphic > to two of the groups discovered by Thompson. This is the beginning > (low dimensional part) of the formalization of the already known > relation between coherence questions and Thompson's groups. From rrosebru@mta.ca Mon Sep 11 12:48:21 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA25253 for categories-list; Mon, 11 Sep 2000 11:48:57 -0300 (ADT) X-Authentication-Warning: shaula.Mathematik.Uni-Marburg.DE: tschroed owned process doing -bs Date: Mon, 11 Sep 2000 15:39:51 +0200 (MET DST) From: Tobias Schroeder X-Sender: tschroed@shaula To: categories@mta.ca Subject: categories: Pullback preserving Set-functors 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 KAA25210 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 4 I'm interested in proofs of or counterexamples for the following conjectures: Conjecture 1: Any Set-endofunctor that preserves kernels (i.e. pullbacks of a mapping with itself) preserves pullbacks. Conjecture 2: Any Set-endofunctor that preserves kernels *and inverse images* (i.e. pullbacks where one of the mapping is injective) preserves pullbacks. Conjecture 3: Same as Conj. 2 with *and inverse images* replaced by *and equalizers*. Conjecture 4: Same as Conj. 1-3, but concerning *weak* preservation. Conjectur 5: Same as 1-4, but for Set-endofunctors that are subfunctors of a pullback preserving functor. I tried to prove these facts in several ways but was not able to do it or to find a counterexample (the answer to this questions is of some relevance for my work on coalgebras) ... and it looks quite easy, doesn't it? Can somebody help me in this? Thank you very much in advance Tobias Schröder -------------------------------------------------------------- Tobias Schröder FB Mathematik und Informatik Philipps-Universität Marburg WWW: http://www.mathematik.uni-marburg.de/~tschroed email: tschroed@mathematik.uni-marburg.de From rrosebru@mta.ca Tue Sep 12 13:11:52 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA26187 for categories-list; Tue, 12 Sep 2000 11:47:30 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200009111742.SAA08419@dumpling.dcs.ed.ac.uk> X-Mailer: exmh version 2.1.1 CVS 2000/03/22 To: categories@mta.ca Subject: categories: Chair in Theoretical Computer Science at Edinburgh University Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Mon, 11 Sep 2000 18:42:26 +0100 From: Gordon Plotkin Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 5 A Chair in Theoretical Computer Science is available in the Division of Informatics at the University of Edinburgh. For further particulars and details of application procedures, see: http://www.informatics.ed.ac.uk/events/vacancies/306712.html Please note that the closing date is October the 13th. From rrosebru@mta.ca Tue Sep 12 13:11:54 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA29457 for categories-list; Tue, 12 Sep 2000 11:41:18 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 11 Sep 2000 17:48:51 -0400 (EDT) From: Peter Freyd Message-Id: <200009112148.e8BLmpT01988@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: re: Pullback preserving Set-functors Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 6 Tobias Schroeder asks: Conjecture 1: Any Set-endofunctor that preserves kernel pairs [He called them "kernels"] preserves pullbacks. Counterexample: the functor that sends the empty set to the empty set and everything else to a fixed one-element set. (Note that this is also a counterexample for the conjecture-5 modification.) Conjecture 2: Any Set-endofunctor that preserves n kernel pairs *and inverse images* (i.e. pullbacks where one of the mapping is injective) preserves pullbacks. Proof: Given such a functor, T:A --> B, where A and B are sufficiently nice categories, lift it to T:A --> B/T1 to obtain a functor that not only preserves kernel-pairs and inverse images but the terminator. It suffices to prove that this lifted T preserves pullbacks (using the fact that the forgetful functor B/T1 --> B preserves pullbacks). hence it suffices to consider the conjecture assuming that the functor preserves also the terminator. A well-known argument then reduces the question to the preservation of binary products. (One may construct equalizers using inverse images and products and from there to arbitrary pullbacks is ancient. See 1.43 in Cats and Allegators.) What we will use is that the functor preserves inverse images and iterated products. Given sets X and Y we know that the product diagram: (X+Y)x(X+Y) / \ [add your own downwards arrowheads] X+Y X+Y is carried to a product diagram T((X+Y)x(X+Y)) / \ T(X+Y) T(X+Y). Using three inverse-image diagrams obtain: XxY / \ Xx(X+Y) (X+Y)xY / \ / \ X (X+Y)x(X+Y) Y \ / \ / X+Y X+Y Now apply T: T(XxY) / \ T(Xx(X+Y)) T((X+Y)xY) / \ / \ TX T((X+Y)x(X+Y)) TY \ / \ / T(X+Y) T(X+Y) As already observed, the very bottom / \ is a product diagram. Each rombus is an inverse-image pullback, hence preserved. Thus the top / \ / \ a product diagram. Conjecture 3: Same as Conj. 2 with *and inverse images* replaced by *and equalizers*. Inverse images of regular subobjects (that is, those that appear as equalizers) are regular: the equalizer of x,y under a map f is the equalizer of xf,yf. Hence if every subobject is regular than preservation of equalizers implies preservation of inverse images. From rrosebru@mta.ca Tue Sep 12 13:15:39 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA24021 for categories-list; Tue, 12 Sep 2000 11:41:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <14782.12062.897526.687526@zermelo.dcs.ed.ac.uk> Date: Tue, 12 Sep 2000 14:26:54 +0100 (BST) From: David Aspinall To: categories@mta.ca Subject: categories: Job: post doc researcher in type systems at LFCS, Edinburgh X-Mailer: VM 6.72 under 21.1 (patch 9) "Canyonlands" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 7 POSTDOCTORAL RESEARCHER IN TYPE SYSTEMS FOR PROGRAMMING LANGUAGES Laboratory for Foundations of Computer Science Division of Informatics University of Edinburgh Project Summary: ================ The project has the following principal objectives: - To design new type systems encompassing algorithms and uses of data structures which fall into desirable feasible complexity classes, but which are prohibited by current such systems. - To extract explicit resource bounds and certificates from typing derivations. - To investigate applications of the new type systems for compiler technology. To explore applications to non-functional programming, e.g., OOP. The full project description at http://www.dcs.ed.ac.uk/home/mxh/epsrc_project.ps provides background material and further details. Candidates: =========== All candidates should hold or soon complete a PhD in a related area of Computer Science, for instance type systems, programming language semantics, complexity theory related to programming languages, compilation of functional programs. Further details and application procedure: ========================================== See http://www.personnel.ed.ac.uk/FURPARTS/Acrel/306739.htm for further details and application procedure. Applications must be via the Personnel Department, 9-16 Chambers Street, Edinburgh, EH1 1HT. UK Tel: +44 (0)131 650 2260 Fax: +44 (0)131 650 6509 Quote reference number: 306739 Closing date is 3 October 2000. We cannot guarantee to consider late applications. Start date is as soon as possible after 1 October 2000. Informal enquiries may be made to Dr Martin Hofmann by email to mxh@dcs.ed.ac.uk From rrosebru@mta.ca Tue Sep 12 21:05:35 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id UAA13191 for categories-list; Tue, 12 Sep 2000 20:26:39 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 12 Sep 2000 12:39:14 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: TTT now available free Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 8 Toposes, Triples and Theories, by Michael Barr and Charles Wells, was published in 1984 by Springer-Verlag as Grundlehren der mathematischen Wissenschaften 278. That version is now out of print. We have retrieved the copyright and have placed a corrected and somewhat expanded version of the book on line, by ftp at ftp.math.mcgill.ca in the files pub/barr/tttdvi.zip pub/barr/tttpdf.zip pub/barr/tttps.zip and by browser from the location http://www.cwru.edu/artsci/math/wells/pub/ttt.html --Michael Barr and Charles Wells From rrosebru@mta.ca Wed Sep 13 15:33:04 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA07503 for categories-list; Wed, 13 Sep 2000 13:35:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 13 Sep 2000 18:19:13 +0200 Message-Id: <200009131619.SAA07317@tosca.dmi.unict.it> From: Vladimiro Sassone To: categories@mta.ca Subject: categories: Lipari Summer School 2001 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 [[ -- Apologies for multiple copies of this message -- \vs ]] First Announcement Foundations of Wide Area Network Programming ============================================ 13th International School for Computer Science Researchers Lipari Island, July 1-14, 2001 The 13th School for Computer Science Researchers addresses Ph.D. students and young researchers who want to get exposed to the forefront of research activity in the field of Wide Area Network Programming, with particular reference to the future of the World Wide Web and to issues of distributed architectures, software engineering, object oriented design, security, mobility, coordination, collaborative work and retrieval/handling of semistructured data. The school will be held in the beautiful surroundings of the island of Lipari. Participants will be arranged in a comfortable hotel at very special rates. The conference room (in the same hotel) is air conditioned and equipped with all conference materials. Special areas are reserved to students for the afternoon coursework and study. A proficiency final exam at the end of each chosen course is mandatory for students. A social tour to Stromboli with spectacular vulcano fireworks will be held on Sunday, July 8. The official language is English. The island of Lipari can be easily reached from Milazzo, Palermo, Naples, Messina and Reggio Calabria by ferry or hydrofoil (50 minutes from Milazzo). The organization provides a round-trip bus from Catania airport (the third most important airport in Italy) to Milazzo hydrofoil terminal and viceversa. Lipari International School Web Pages ===================================== http://lipari.dmi.unict.it/Lipari/index.asp Courses (incomplete list) ======================== * Security Protocols and Formal Methods. Martin Abadi Bell Labs Research, Palo Alto abadi@research.bell-labs.com http://pa.bell-labs.com/~abadi/home.html * Principles of Wide Area Programming. Luca Cardelli Microsoft Research, Cambridge, UK luca@microsoft.com http://www.luca.demon.co.uk/ * The Coordination Paradigm. Paolo Ciancarini Universitā degli Studi, Bologna ciancarini@cs.unibo.it http://www.cs.unibo.it/~cianca/ * Concurrent Object-Oriented Programming. Doug Lea State University of New York at Oswego dl@cs.oswego.edu http://gee.cs.oswego.edu/dl/ * Mobility, Security and Proof-Carrying Code. Peter Lee Carnegie-Mellon University, Pittsburgh petel@cs.cmu.edu http://www.cs.cmu.edu/~petel/ * Java, Jini and Related Technologies. Jim Waldo Sun Microsystems, Burlington, Mass. and Harvard University jim.waldo@sun.com Directors ========= Alfredo Ferro (University of Catania), Co-chair Ugo Montanari (University of Pisa), Co-chair Vladimiro Sassone (University of Catania), Co-chair Advanced Seminars ================= A few talks will be given by auditors or by experts visiting the School for short periods. Application =========== Two kinds of partecipants are welcome. Students: Partecipants who are expected to do afternoon courseworks and take a final exam. Auditors: Partecipants who are not interested in taking the final exam. Up to 60 students and a limited number of additional auditors will be admitted. Deadline for application is March 31, 2001. Applicants must include a short curriculum vitae and specify two professors whom letters of recommendation will be asked to, if deemed necessary. Applicants will be notified about admission by April 14, 2001. Registration fee is 400 U.S. dollars (includes bus+hydrofoil Catania airport-Lipari-Catania airport, social tour to Stromboli, approx. 1000 pages of xeroxed course material). While electronic application is preferred, applications by mail to the following address will also be accepted: School Director: Prof. Alfredo Ferro Dipartimento di Matematica e Informatica Universitā degli Studi di Catania - Cittā Universitaria Viale A.Doria, 6 - 95125 Catania - ITALY Tel: +39 095 221012 / +39 095 7383071 Fax: +39 095 7337032 E-mail: ferro@dmi.unict.it Important dates =============== Deadline for application: March 31, 2001. Notification of admission: April 14, 2001. Lipari School: July 1-14,2001 From rrosebru@mta.ca Wed Sep 13 15:33:45 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA09733 for categories-list; Wed, 13 Sep 2000 14:00:09 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <000d01c01c79$83f70b40$237079a5@osherphd> From: "Osher Doctorow" To: Subject: categories: Fixed points of cross-category relationship - Doctorow Date: Mon, 11 Sep 2000 22:22:01 -0700 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.50.4133.2400 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 10 From: Osher Doctorow, Ph.D. osher@ix.netcom.com, Monday Sept. 11, 2000, 10:02PM Consider the fixed point g(x,y) = (x,y) for g(x,y) = (x-->y, (x-->y)^) where x-->y is 1 - x + y and its real conjugate, labeled (x-->y)^, is 1 + x - y. This is equivalent to 1 - x + y = x, 1 - y + x = y, and subtracting the second equation from the first results in -x + y + y - x = x - y or 3(y - x) = 0 so y = x and substituting for either x or y in the first or second equation yields the unique solution x = 1, y = 1, so the fixed point is (1, 1), and since x-->y = x and y-->x = y, we also have x-->y = 1 and y-->x = 1. It turns out that even if the problem had been g(x,y) = (y,x) for the above g, the same fixed point would have been obtained. This is remarkable for those interested in fixed points. Fixed points have turned out to be of considerable importance across categories, and similarly for symmetry groups and invariance properties, both in mathematics and physics. From the above paragraph, the multiplicative unit of the category has turned out to be its unique fixed point. Also it suggests that categories for which the multiplicative unit is very important are those in which x-->y = 1 - x + y plays an important role. This holds for at least two categories, which I will refer to for short as probabilities and (fuzzy) multivalued logic - especially Product/Goguen logic and Lukaciewicz logic, although both are related to Godel logic. The multiplicative unit is important in probability because probabilities by definition are between 0 and 1 - their multiplicative unit is also their maximum. In (fuzzy) multivalued logics, the unit 1 is similarly an extreme value, although it is usually considered to be the "trivial" case of either tautology or contradiction (usually tautology). This would at least preserve the intuitive idea of tautology expressing "complete logical truth", however trivial we may consider that to be. The above results also suggest that a generalization of fixed point results to the general case where x-->y and/or y-->x = 1 might be quite useful, and this is precisely what logic-based probability (LBP) has found to be the case (recall my previous contributions to categories@mta.ca). There is an interesting application to history that I might cite as an amusing aside. History is usually taught in terms of stories - the story of a war, a civilization, an era, etc. The above results would suggest, if they are applicable to history, that it is best to teach history as the study of rare discrete events and how they causally influence each other. For example, what caused a war, what ended a war, or in different language, why did the war occur, why did the war end, etc. The discrete events would correspond to fixed points, and we would be especially interested in them when they are repeated in history - the repetition would correspond to fixed points or invariance in time or symmetry in time. Then history would become the study of why errors repeat rather than merely the study of what happened, where it happened, who it happened to, how it happened, etc. I find this somewhat amusing because of arguments that one can get into when discussing matters with the more detail-obsessed historians to whom any suggestion of causation or relationships across categories results sometimes in remarkable responses. Osher Doctorow From rrosebru@mta.ca Thu Sep 14 17:53:51 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA25422 for categories-list; Thu, 14 Sep 2000 16:23:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <39C0D48E.70979189@loria.fr> Date: Thu, 14 Sep 2000 15:37:18 +0200 From: Francois Lamarche Organization: LORIA X-Mailer: Mozilla 4.7 [en] (X11; I; Linux 2.2.13 i686) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: A universal property for the ordinal Omega? Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 11 Has anybody ever proved the following result? In the category of posets the initial algebra with the following operations: 1- a constant 0 2- an inflationary successor s : x \le sx 3- sups of omega-Chains is the least non-denumerable ordinal Omega. This seems to be a pretty natural question to ask, so it must have been done before. Francois Lamarche From rrosebru@mta.ca Fri Sep 15 12:44:53 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA26336 for categories-list; Fri, 15 Sep 2000 11:30:40 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <39C22090.5802016D@informatik.uni-bremen.de> Date: Fri, 15 Sep 2000 15:13:52 +0200 From: Lutz Schroeder X-Mailer: Mozilla 4.75 [en] (X11; U; SunOS 5.7 sun4m) X-Accept-Language: en MIME-Version: 1.0 To: Categories Subject: categories: question on "model functor" Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 The following question looks so natural that somebody's bound to have looked into it: Does the functor Cat^op ---> CAT A |--> [A,Set] reflect isomorphisms (more generally: limits)? related questions (i.e. ones that would solve the problem or at least help solving it) are -- Are epimorphisms in Cat those functors F:A-->B for which F[A] generates B by composites and inverses of isomorphisms (in B)? -- is the source of all covariant hom-functors an extremal mono-source in CAT? The answers are probably in the literature - but where? Thanks a lot, Lutz Schroeder -- ----------------------------------------------------------------------------- Lutz Schroeder Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3550 University of Bremen lschrode@informatik.uni-bremen.de P.O.Box 330440, D-28334 Bremen http://www.informatik.uni-bremen.de/~lschrode ----------------------------------------------------------------------------- From rrosebru@mta.ca Sun Sep 17 12:15:29 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA30488 for categories-list; Sun, 17 Sep 2000 11:14:52 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: question on "model functor" Date: Fri, 15 Sep 2000 18:08:14 +0100 (BST) To: categories@mta.ca (Categories) In-Reply-To: <39C22090.5802016D@informatik.uni-bremen.de> from "Lutz Schroeder" at Sep 15, 2000 03:13:52 PM X-Mailer: ELM [version 2.5 PL2] 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: X-Keywords: X-UID: 13 > The following question looks so natural that somebody's > bound to have looked into it: > > Does the functor > > Cat^op ---> CAT > > A |--> [A,Set] > > reflect isomorphisms (more generally: limits)? The question is not very well posed: since Cat and CAT are 2-categories, one ought to be asking about whether it reflects equivalences. For this, the answer is negative (and well known): a functor A --> B induces an equivalence [B,Set] --> [A,Set] iff it induces an equivalence between the idempotent-completions of A and B. So the inclusion of any non-idempotent- complete category in its idempotent-completion provides a counterexample. However, if you insist on asking about isomorphisms rather than equivalences, the answer is yes. It's easy to see that if F: A --> B fails to be surjective (resp. injective) on objects then the induced functor [F,Set] fails to be injective (resp. surjective); so if [F,Set] is an isomorphism then F must be bijective on objects, and this combined with inducing an equivalence of idempotent-completions is enough to make it an isomorphism. But this is not a very meaningful result. Provided you assume a sufficiently powerful form of the axiom of choice, [A,Set] and {B,Set] will be isomorphic whenever they are equivalent (since each has a proper class of objects in each isomorphism class, except for the initial object which is unique in its isomorphism class). The isomorphism will not, of course, be induced by a functor from A to B; but it will be naturally isomorphic to a functor that is (at least provided B is idempotent-complete). Peter Johnstone From rrosebru@mta.ca Sun Sep 17 12:15:32 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA05681 for categories-list; Sun, 17 Sep 2000 11:34:09 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 16 Sep 2000 08:22:36 -0400 (EDT) From: Marta BUNGE To: categories@mta.ca Subject: categories: The Dubuc Topos Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 14 In response to the note by Eduardo Dubuc, I would like to urge the workers in the field of SDG who use this topos (and it is hardly easy to avoid doing so!) to name it the "Dubuc topos". I myself have used several other names for it, such as G (for germ determined) or \tilde(B^op) for the site of definition, and this includes my papers in the JPPA on Synthetic Aspects of C-infinity mappings (one with F. Gago), my paper with M. Heggie in Contemporary Mathematics, and even in our joint paper B-D, Local concepts, where we called it G. In fact, this is perfectly appropriate and I always referred to the sources. Therefore, it may thus seem like a strange request, and even more strange that I agree to this request at this point (assuming that I will ever write anything again in SDG!), but I understand it perfectly. It is annoying to see one's work being appropriated by others who, little by little contribute to the obliteration of any direct reference (except pro forma) to the originator of these ideas. This is definitely wrong and has done damage which may not be too late to repair. I have been a witness to the developments that Eduardo Dubuc relates in his note and I herewith corroborate their authenticity. Moreover, I have related these very facts to many people, including one of the authors of the Moerdijk-Reyes team, who blamed the other one for it! I have also said as much in refereeing papers by the Moerdijk-Reyes team, with copies to the authors. This is not a fib of someone's imagination, as may be easy to infer not knowing the facts or the people involved. Something has now triggered it all back, it is unimportant what did it. What matters is that this sad and obscure aspect of the history of categories and of our group has never come up into the open. Now that the author himself has felt the need to do so, I have no problem supporting him and wishing that at least from now on his work will be given the credit it deserves. Marta Bunge From rrosebru@mta.ca Fri Sep 15 12:52:31 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA11098 for categories-list; Fri, 15 Sep 2000 11:28:38 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Todd Wilson MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <14785.17898.355177.662128@goedel.engr.csufresno.edu> Date: Thu, 14 Sep 2000 14:40:58 -0700 (PDT) To: categories@mta.ca Subject: categories: Re: A universal property for the ordinal Omega? In-Reply-To: <39C0D48E.70979189@loria.fr> References: <39C0D48E.70979189@loria.fr> X-Mailer: VM 6.75 under 21.1 (patch 3) "Acadia" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 On Thu, 14 Sep 2000, Francois Lamarche wrote: > Has anybody ever proved the following result? > > In the category of posets the initial algebra with the following > operations: > > > 1- a constant 0 > > 2- an inflationary successor s : x \le sx > > 3- sups of omega-Chains > > > is the least non-denumerable ordinal Omega. The least non-denumerable ordinal is usually called omega_1, and even though the result you are after is not directly stated in the book A. Joyal, I. Moerdijk, Algebraic Set Theory, LMS Lect Notes 220, Cambridge University Press, 1995, this book is clearly relevant to your question. Joyal and Moerdijk, in a tour de force, construct a number of free algebras for various kinds of successor operation and "small"-indexed sups, for a quite general notion of "small" that includes the kind of cardinality restriction to which you refer. --------------------------------------------------------------------------- Todd Wilson A smile is not an individual product; Computer Science Department it is a co-product. California State University, Fresno -- Thich Nhat Hanh --------------------------------------------------------------------------- From rrosebru@mta.ca Fri Sep 15 12:55:50 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA25919 for categories-list; Fri, 15 Sep 2000 11:26:52 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: From: edubuc@dm.uba.ar (Eduardo Dubuc) Subject: categories: models of SDG To: categories@mta.ca Date: Thu, 14 Sep 2000 18:16:43 -0300 (ARG) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 GERM DETERMINED IDEALS AND WELL ADAPTED MODELS OF SDG I write this note because I feel it is time to let know explicitly to the category theory community the following situation, and to make a request. In a recent paper on SDG "Super smooth topoi, by H. Nishimura" one can read the following: "Therefore we must build our model theory of Synthetic Supergeometry not directly after the standard manner of Moerdijk & Reyes [1991] [*] but after the manner of Dubuc-Taubin [1983]". Now, this "standard manner" of building models was developed by Dubuc and not by Moerdijk-Reyes. (in [1983] I developed also the analytic model, which does not correspond to an algebraic theory in the Lawvere sense, and can not be done as the differential models which correspond to C-infinity rings). [*][M-R] "Models of Smooth infinitesimal Analysis", Moerdijk and Reyes, Springer Verlag 1991. Of course, I understand that when a monograph is available, the proper reference is that, and not the original papers. But, phrases as the one quoted above are ambiguous, and at fault is not Nishimura. I shall resume the history of the subject: In a series of papers and many lectures given specially in Montreal, Sydney, Oberwolfach and elsewhere I created and started the developement of the subject of models of SDG adapted (or well adapted as I call them) for the applications to classical differential geometry. [1] Sur les Modeles de la Geometrie Differentielle Sinthetyque, "Cahiers de Topologie et Geometrie Differentielle" Vol. XX-3 (1979). [2] Schemas C-inf (amplified version of [3], with detailed proofs and many examples), "Prepublications de la Universite de Montreal" 80-81 edited by G. Reyes (1980). [3] C-inf Schemes, "American Journal of Mathematics", John Hopkins University, Vol. 103-4 (1981). [4] Open Covers and Infinitary Operations in C-inf-rings, "Cahiers de Topologie et Geometrie Differentielle" Vol. XXII-3 (1981). [5] Archimedian Local C-inf-rings and Models of SDG (with Marta Bunge), "Cahiers de Topologie et Geometrie Differentielle" Vol. XXVII-3 (1986). [6] Germ representability and Local integration of vector fields in a well adapted model of SDG, "Journal of Pure and Applied Algebra" Vol. 64 (1990). A) I introduced the notion of well adapted models and constructed the first ones. B) I started a systematic study of C-infinity rings as such. Of course, they were already there, but nothing had been done with them. I had to state and prove even such simple facts as that the algebraic quotient of a C-infinity ring by an R-algebra ideal had a canonical structure of C-infinity ring, and was then the quotient in this category. I introduced the notion of Germ Determined Ideal (or ideal of local nature), which was, as such, nowhere to be found in the literature, and stated and proved their basic properties. This, I think, is the most important concept in the subject. It is the basic definition to start to build upon. It is just the right concept needed. Among other things, I first proved it contains all finitely generated ideals, and defines the largest possible class of C-infinity rings consistent with the nullestelentsatz. This means that the ring can be seen as the ring of global sections of a C-infinity Scheme. The notion of germ determined ideal also determines the right notion of C-infinity local ring (notice that I do not say local C-infinity ring), that I then developed. I also developed the relative C-infinity version of inverting elements universally, and proved that the ring of C-infinity functions defined in an open set U inverts universally a function which is non-zero exactly on U (every Euclidean open is C-infinity Zariski). Etc, etc, all the basic structure of the C-infinity relative version of algebraic geometry. Now, [M-R] write "Although this general notion of C-infinity ring does not occur as such in classical analysis and differential geometry, the main examples do ... Given the role of these examples of C-infinity rings in the classical literature, it is not surprising that although the statements of several of the results in this chapter seem new, most of their proofs are either known or easily derivable from known ones". This is, at the least, misleading, and can also be applied to many important concepts in mathematics. Of course, when the new concepts are introduced, the examples are already there, and the proof of the basic properties is easy. [M-R] ignore the fact that the important thing is to identify explicitly the concept, and to identify the right statements. And this does not come easily. And I repeat, even if C-infinity rings may have been there, the concept of germ determined ideal was not, and derived concepts and the statments of their basic essential properties could not even be there. C) With this in hand, I introduced the Topos G of sheaves for the open covering topology on the dual of the category of C-infinity rings presented by a germ determined ideal, and proved all the basic important properties, which many times are the correct relative C-infinity versions of corresponding properties in algebraic geometry. This topos is the best known model in order to do applications of SDG to classical differential geometry, and as such, it is the most utilized in practice. Many early workers in the subject (J. Penon, O. Bruno, F. Gago, Yetter, among others) called this topos "The Dubuc Topos". Even Moerdijk and Reyes did so in some preprints, although they changed this in the published version. Now, [M-R] write "As far as terminology is concerned, we have tried to avoid descriptions of the type "the Moerdijk envelop of the Reyes topos", in favor of more informative ones". But the true fact was that the only name that was involved was "Dubuc", since no other new name was being utilized at the time (of course, things as Kock-Lawvere Axiom or Weil algebras were not aimed by this philosophy, and "Moerdijk envelop of the Reyes topos" was an invention). D) I should mention here that I do not ignore the fact that my work is acknowledged and referenced in the monograph [M-R], and that this can be proved in a court of Law. The matter is much more subtle, and nobody can deny the evidence of the following consequence of this maneuvering: A consequence of this maneuvering is that my name, as time passes, and as young people appear, is less and less associated with a subject that I created and developed in large part. Namely, models of SDG adapted to classical differential geometry. People talk as if the well adapted models were always there, or start referring to them in a way that may lead inexperienced (in the subject) readers to believe that these constructions are "M-R way of doing models", as I quoted at the beginning of this note. This is what it is actually happening, and no arguing can deny it. E) This does not do justice to my work, and does not corresponds to the true history of the subject. As an starting point to remedy it, I request all workers that need to use the topos G, to refer to it as "Dubuc Topos". After all, it is a long tradition in mathematics to associate proper names to important concepts or constructions when it is justified, as I believe it is the case here. Eduardo J. Dubuc Buenos Aires, September 2000. From rrosebru@mta.ca Mon Sep 18 09:11:07 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA30105 for categories-list; Mon, 18 Sep 2000 08:22:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sun, 17 Sep 2000 12:37:14 -0400 (EDT) From: Peter Freyd Message-Id: <200009171637.e8HGbEg17088@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: question on "model functor" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 Lutz Schroeder asked: Does the functor Cat^op ---> CAT A |--> [A,Set] reflect isomorphisms (more generally: limits)? Peter Johnston's answer to the first question is the right one, but one could expand. There's no doubt that his argument works well for small categories (which, I take it, is what was intended by the notation), there's a little worry about it working for _locally_ small categories, and there's no hope at all that it works for arbitrary categories, even if we restrict to those categories with small numbers of objects. (As for the second -- parenthetical -- question: see the bottom.) For the fun of it, consider the one-object category whose maps are named by pairs where X is a finite set and f is a permutation thereon. I'll say that and name the same map if the supports of f and g are both contained in the intersection of X and Y, and further, when f and g are restricted to that intersection, they become equal. Given the names of any two maps, one can always choose names with the same first coordinates and that's enough to tell you how to compose them. There's a functor from this big one-object category to the tiny one- object category usually called the group, Z_2, to wit, the signature functor. This functor is carried by [-,Set] to an isomorphism in CAT. Also for the fun of it, here's a proof for locally small categories that doesn't require considering things like small projectives in super-big categories. It's routine to reduce to the case where T may be assumed the be the inclusion functor of a lluf subcategory (one that contains all identity maps) *A* into a category *B*. The next step is to show that *A* is a retract of *B*. For any object A, let H^A denote the covariant set-valved functor on *A* represented by A. Assuming that [T,Set] is an isomorphism, let G^A be the unique extension of H^A to *B*. For any f:A -> X in *A* and g:X -> Y in *B* (G^A'g)'(f) is a map in *A* from A to Y. Note that this is not defined as a composition of maps (indeed, G^A'g is not defined as a map in any category other than the category of sets) but as the application of a function G^A'g on an element f in G^A'X, hence I will avoid using catenation for other than composition by inserting prime-marks (for application). The functoriality says that for h:Y -> Z we have 1: (G^A'h)'((G^A'g)'f) = (G^A'(hg))'f (and, of course, (G^A'1)'(f) = f). Now let j:B -> A be a map in *A*. The natural transformation H^j extends uniquely to a transformation G^j. But since the two Gs do the same thing to objects as the two Hs we know that G^j and H^j do the same thing to those objects. We have, therefore, 2: ((G^A'g)'(f))(j) = (G^B'g)'(fj). Construct U:*B* --> *A* by defining U(g) = (G^X'g)'1 for g:X -> Y. For h:Y -> Z in *A* we have (using 1) U(hg) = (G^X'(hg))'1 = (G^X'h)'((G^X'g)'1) = (G^X'h)'(Ug) and (using 2) the later is equal to (G'X'h)'(1Ug) = (G^Y'h)'1)(Ug) = (Uh)(Ug). Consider the two endo-functors on *B*, the identity functor and the idempotent *B* --> *A* --> *B*. The hypothesis that [T,Set] is an isomorphism says that for any set-valued F on *B* it is the case that F is equal to *B* --> *A* --> *B* --> Set. But the set-valued functors (indeed, just the representables) are collectively faithful, and that forces *B* --> *A* --> *B* to be the identity functor, which, in turn, forces each of *B* --> *A* and *A* --> *B* to be identity functors. The later functor is the given T. Finally, as for the question about reflecting limits: if I may quote Cats and Alligators: "It seems to be a general principle that almost any property of interest is reflected by [isomorphism-reflecting embeddings] that preserve it" (1.33) In particular there's an easy argument for the case of limits in a complete category because a cone on a diagram fails to be a limit precisely when the induced map from the limit fails to be an isomorphism. From rrosebru@mta.ca Tue Sep 19 17:19:35 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA00933 for categories-list; Tue, 19 Sep 2000 16:10:09 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: models of SDG To: categories@mta.ca Date: Tue, 19 Sep 2000 13:03:10 -0500 (CDT) From: "David Yetter" X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20000919180310.C5AAC860C@euler.math.ksu.edu> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 18 Does anyone have a full citation to the Nishimura paper which Dubuc justly criticizes for misattributing his construction? I am interested because the title, and lack of care with citations, suggest the possibility that Nishimura is simply reproving results from my paper D.N. Yetter, "Models for Synthetic Supergeometry", Cahier de Top. et Geom. Diff. Cat. 29 (2) (1988) 87-108. In that paper, I constructed "super" analogues of both the Dubuc and Stein toposes, and examined some of their properties in light of the then-extant understanding of SDG and supergeometry. David Yetter From rrosebru@mta.ca Tue Sep 19 17:19:37 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA04087 for categories-list; Tue, 19 Sep 2000 16:09:20 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 19 Sep 2000 11:58:44 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Dave Harrison Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 19 I have just received from Ann Harrison the sad news that Dave died last Dec. 21. I suspect that most of the younger practitioners of category theory are not aware of Dave's contributions to the subject. Not in the sense of having actively worked on it, but of having encouraged it in the very early days. When he came to Penn he taught a course in homological algebra that used categories extensively. In point of fact, I had never heard of a category before taking that course. Then he was one of the main organizers of the La Jolla conference in 1965 that was the first ever major international conference in categories. (The first conference that I am aware of was the midwest category meeting that Saunders Mac Lane organized in April (I think) of the same year, a few months earlier. But the participants consisted only of a handful of people from Urbana and Chicago.) For anyone who wishes to write Ann, her address is 12 Striper Lane, Chatham, MA 02633. Michael From rrosebru@mta.ca Tue Sep 19 17:25:34 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA08038 for categories-list; Tue, 19 Sep 2000 16:08:51 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200009191437.AA26630@menthe.ens.fr> Mime-Version: 1.0 (NeXT Mail 4.2mach_patches v148.2) Content-Type: multipart/alternative; boundary=NeXT-Mail-195190528-4 Content-Transfer-Encoding: 7bit From: Giuseppe Longo Date: Tue, 19 Sep 2000 16:37:31 +0200 To: categories@mta.ca Subject: categories: New programs ... conference Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 20 --NeXT-Mail-195190528-4 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline "New programs and open problems in the foundation of mathematics and of its = applications, in year 2000"=20 November 13 and 14, 2000 Ecole Normale Sup=E9rieure, 45, rue d'Ulm, 75005 Paris Salle Dussane =A0=A0=A0=A0=A0=A0=A0Monday, November 13 :=20 14h : =A0=A0=A0J.-Y. Girard (CNRS, Marseille): "Locus solum"=20 Respondent: P.-L. Curien (CNRS - Univ. Paris VII)=20 15h 30 : =A0=A0=A0A. Macintyre (Univ. Edinburgh): "Prospects in logic"=20 Respondent: A. Marcja (Univ. Firenze) 17h : PAUSE.=20 17h 15 : =A0=A0=A0W. Lawvere (SUNY, Buffalo): "Dialectical foundations of, = by, and for mathematics" =20 Respondent: I. Moerdijk (Univ. Utrecht)=20 =A0=A0=A0=20 =A0=A0=A0=A0=A0=A0=A0Tuesday, November 14 : =20 9h 30 : =A0=A0=A0R. Milner (Univ. Cambridge): "The flux of computation"=20 Respondent: G. Berry (Ecole des Mines, Sophia-Antipolis)=20 11h : =A0=A0=A0G. Parisi (Univ. Roma I): "Six spaces looking for a = geometer"=20 Respondent: J.-P. Nadal (CNRS-ENS, Paris) =20 =A0=A0=A0=A0=A0=A0=A0Tuesday afternoon : =20 14h 30 : =A0=A0=A0A. Connes (Coll=E8ge de France, Paris): "Non-commutative = Geometry" =20 Respondent: C. Soul=E9 (IHES, Paris);=20 =A0=20 Panel discussion :=20 "Geometric Structures in Logic, Physics and Computing" with the invitees = and the=20 members of the working group "G=E9om=E9trie et Cognition" (G. Longo, = CNRS-ENS, chair)=20 ------------------=20 The Conference is one of the activites promoted by the "Atelier de = Recherche" G=E9om=E9trie et Cognition ( = http://www.dmi.ens.fr/users/longo/geocogni.html ) =20 financed by the french Ministry of Research, and it is partly supported = also by the Laboratoire d'Informatique=20 de l'ENS (LIENS, CNRS).=20 The Conference is open to public (no attendance fees) and the organizers = can provide no help to attendees=20 (a list of hotels may be found in : = http://www.dmi.ens.fr/users/longo/GeoCo-fold/hotels.html ).=20 =A0http://www.dmi.ens.fr/users/longo/GeoCo-fold/new-programs.html =A0=20 --NeXT-Mail-195190528-4 Content-Type: text/enriched; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
"New programs and open problems in the foundation of mathematics and of its applications, in year 2000"=20
=20 November 13 and 14, 2000 Ecole Normale Sup=E9rieure, 45, rue d'Ulm, 75005 Paris Salle Dussane
=A0=A0=A0=A0=A0=A0=A0Monday, November 13 :=20 14h : =A0=A0=A0J.-Y. Girard (CNRS, Marseille): "Locus solum"=20 Respondent: P.-L. Curien (CNRS - Univ. Paris VII)=20 15h 30 : =A0=A0=A0A. Macintyre (Univ. Edinburgh): "Prospects in logic"=20 Respondent: A. Marcja (Univ. Firenze) 17h : PAUSE.=20 17h 15 : =A0=A0=A0W. Lawvere (SUNY, Buffalo): "Dialectical foundations of, by, and for mathematics" =20 =20 Respondent: I. Moerdijk (Univ. Utrecht)=20 =A0=A0=A0=20 =A0=A0=A0=A0=A0=A0=A0Tuesday, November 14 : =20 =20 9h 30 : =A0=A0=A0R. Milner (Univ. Cambridge): "The flux of computation"=20 Respondent: G. Berry (Ecole des Mines, Sophia-Antipolis)=20 11h : =A0=A0=A0G. Parisi (Univ. Roma I): "Six spaces looking for a geometer"=20 Respondent: J.-P. Nadal (CNRS-ENS, Paris)=20 =20 =A0=A0=A0=A0=A0=A0=A0Tuesday afternoon :=20 =20 14h 30 : =A0=A0=A0A. Connes (Coll=E8ge de France, Paris): "Non-commutative Geometry" =20 =20 Respondent: C. Soul=E9 (IHES, Paris);=20 =A0=20 Panel discussion :=20 "Geometric Structures in Logic, Physics and Computing" with the invitees and the=20 members of the working group "G=E9om=E9trie et Cognition" (G. Longo, CNRS-ENS, chair)=20
------------------=20
The Conference is one of the activites promoted by the "Atelier de Recherche" G=E9om=E9trie et Cognition=20 ( http://www.dmi.ens.fr/users/longo/geocogni.html ) =20 =20 financed by the french Ministry of Research, and it is partly supported also by the Laboratoire d'Informatique=20 de l'ENS (LIENS, CNRS).=20 The Conference is open to public (no attendance fees) and the organizers can provide no help to attendees=20 (a list of hotels may be found in :=20 http://www.dmi.ens.fr/users/longo/GeoCo-fold/hotels.html ).=20 =A0http://www.dmi.ens.fr/users/longo/GeoCo-fold/new-programs.html =A0 --NeXT-Mail-195190528-4-- From rrosebru@mta.ca Wed Sep 20 13:18:16 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA24728 for categories-list; Wed, 20 Sep 2000 11:45:11 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: From: edubuc@dm.uba.ar (Eduardo Dubuc) Subject: categories: yetter&supernishimura To: categories@mta.ca Date: Tue, 19 Sep 2000 18:53:01 -0300 (ARG) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 i quote from yetter's message: "Does anyone have a full citation to the Nishimura paper which Dubuc justly criticizes for misattributing his construction? I am interested because the title, and lack of care with citations, suggest the possibility that Nishimura is simply reproving results from my paper D.N. Yetter, "Models for Synthetic Supergeometry", Cahier de Top. et Geom. Diff. Cat. 29 (2) (1988) 87-108." Nishimura's paper is titled "Supersmooth Topoi" (I have a only a preprint) It is a well referenced paper. In this paper Nishimura knows and comments on Yetter's (1988). It is actually doing a different thing. He uses my (with Taubin) construction with the notion of analytic ring (1983), which is not to be found in [M-R] monograph. This notion is algebraic but in the sense of a category with finite limits, not in the sense of a category with finite products. (quotients are not suryective to mention a difference) just to clarify my letter, i quote again Yetter above: "Dubuc justly criticizes for misattributing his construction?" Well, Nishimura is using as a reference for my construction the [M-R] monograph, and it is not at fault as I said. The problem is, that it sounds ambigous because a whole situation I described in my letter I quote now again from the [M-R] monograph two references concerning specifically my work, which I found they reveal a lot: "Although this general notion of C-infinity ring does not occur as such in classical analysis and differential geometry, the main examples do ... Given the role of these examples of C-infinity rings in the classical literature, it is not surprising that although the statements of several of the results in this chapter seem new, most of their proofs are either known or easily derivable from known ones". "As far as terminology is concerned, we have tried to avoid descriptions of the type "the Moerdijk envelop of the Reyes topos", in favor of more informative ones" well ... eduardo dubuc From rrosebru@mta.ca Thu Sep 21 12:55:56 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA02389 for categories-list; Thu, 21 Sep 2000 10:49:04 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200009210751.AA27346@menthe.ens.fr> Content-Type: text/plain Mime-Version: 1.0 (NeXT Mail 4.2mach_patches v148.2) From: Giuseppe Longo Date: Thu, 21 Sep 2000 09:51:34 +0200 Subject: categories: Conference: New programs ... 13-14/11/00 To: categories@mta.ca References: <200009201837.e8KIbge09752@saul.cis.upenn.edu> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 22 [Note from moderator: this is a plain ascii version of the earlier post, thanks to the poster for providing this.] "New programs and open problems in the foundation of mathematics and of its applications, in year 2000" November 13 and 14, 2000 Ecole Normale Superieure, 45, rue d'Ulm, 75005 Paris Salle Dussane Monday, November 13: 14h : J.-Y. Girard (CNRS, Marseille): "Locus solum" Respondent: P.-L. Curien (CNRS - Univ. Paris VII) 15h 30 : A. Macintyre (Univ. Edinburgh): "Prospects in logic" Respondent: A. Marcja (Univ. Firenze) 17h : PAUSE. 17h 15 : W. Lawvere (SUNY, Buffalo): "Dialectical foundations of, by, and for mathematics" Respondent: I. Moerdijk (Univ. Utrecht) Tuesday, November 14: 9h 30 : R. Milner (Univ. Cambridge): "The flux of computation" Respondent: G. Berry (Ecole des Mines, Sophia-Antipolis) 11h : G. Parisi (Univ. Roma I): "Six spaces looking for a geometer" Respondent: J.-P. Nadal (CNRS-ENS, Paris) Tuesday afternoon: 14h 30 : A. Connes (College de France, Paris): "Non-commutative Geometry" Respondent: C. Soule (IHES, Paris); 16h : Panel discussion : "Geometric Structures in Logic, Physics and Computing" with the invitees and the members of the working group "Geometrie et Cognition" (G. Longo, CNRS-ENS, chair) ------------------ The Conference is one of the activites promoted by the "Atelier de Recherche" Geometrie et Cognition ( http://www.dmi.ens.fr/users/longo/geocogni.html ) financed by the french Ministry of Research, and it is partly supported also by the Laboratoire d'Informatique de l'ENS (LIENS, CNRS). The Conference is open to public (no attendance fees) and the organizers can provide no help to attendees (a list of hotels may be found in : http://www.dmi.ens.fr/users/longo/GeoCo-fold/hotels.html ). http://www.dmi.ens.fr/users/longo/ From rrosebru@mta.ca Fri Sep 22 20:41:01 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA17312 for categories-list; Fri, 22 Sep 2000 19:21:31 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200009221607.SAA11033@irmast2.u-strasbg.fr> Date: Fri, 22 Sep 2000 18:07:01 +0200 (MET DST) From: Philippe Gaucher Reply-To: Philippe Gaucher Subject: categories: characterisation of nerve of omega-categories To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: L7WxdTqbDzh5UNAygE2ihw== X-Mailer: dtmail 1.3.0 CDE Version 1.3 SunOS 5.7 sun4u sparc Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 Dear all, I don't remember where I could find a characterization for a simplicial set to be the simplicial nerve of some strict globular omega-category ? I think that the characterization is that the simplicial set must be given with a structure of thin elements satisfying some axioms like the filling of horners and thin horners. Could you send me a reference please ? Thank you in advance. pg. From rrosebru@mta.ca Mon Sep 25 00:50:08 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id XAA24962 for categories-list; Sun, 24 Sep 2000 23:39:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from zent.mta.ca (zent.mta.ca [138.73.101.4]) by mailserv.mta.ca (8.9.3/8.9.3) with SMTP id VAA02829 for ; Fri, 22 Sep 2000 21:27:02 -0300 (ADT) X-Received: FROM macadam.mpce.mq.edu.au BY zent.mta.ca ; Fri Sep 22 21:28:55 2000 -0300 X-Received: from hera.mpce.mq.edu.au (hera.mpce.mq.edu.au [137.111.219.13]) by macadam.mpce.mq.edu.au (8.8.8/8.8.8) with ESMTP id LAA17672; Sat, 23 Sep 2000 11:26:52 +1100 (EST) X-Received: from pascal (mpce-remote31.mpce.mq.edu.au [137.111.241.109]) by hera.mpce.mq.edu.au (8.9.3+Sun/8.9.3) with SMTP id LAA18478; Sat, 23 Sep 2000 11:26:50 +1100 (EST) From: "Dominic Verity" To: "Philippe Gaucher" , Subject: categories: RE: characterisation of nerve of omega-categories Date: Sat, 23 Sep 2000 11:26:09 +1000 Message-ID: <000201c024fd$40b58e60$6df16f89@pascal.mpce.mq.edu.au> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook 8.5, Build 4.71.2173.0 Importance: Normal In-Reply-To: <200009221607.SAA11033@irmast2.u-strasbg.fr> X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 Hi Philippe, The answer to your question is that, to my knowledge, the characterisation of the nerves of n-categories currently only exists in conjectural form in the literature. In particular, a full description of this conjecture is given in the paper: "The Algebra of Oriented Simplexes" by Ross Street (JPAA 49 (1987) pp 283-335) and an associated note "Fillers for Nerves" (I forget the precise reference) which proves the necessity of this characterisation. This actual conjecture is originally due to John Roberts - it does involve simplicial sets enriched with a distinguished set of "hollow" or "thin" simplices and appropriate "admissible" horn filler conditions with respect to these thin simplices. Roberts calls these structures "complicial sets". I presented a proof of this conjecture to a conference at UC Berkeley (MSRI) in 1993 (I think) and also in a number of seminars given at Bangor in Wales and at the Sydney Category Seminar, but unfortunately never published the result, due to a subsequent career change (I became an investment banker). Roberts' original conjecture as described by Street does indeed hold - in fact a slightly weaker result may be proved which only involves fillers for "inner" horns. More recently, I have taken some time away from the world of finance and am currently working on writing up my results in this area - which I hope to make available over the next few months. All the very best Dominic Verity Macquarie University Sydney, Australia > -----Original Message----- > From: cat-dist@mta.ca [mailto:cat-dist@mta.ca]On Behalf Of Philippe > Gaucher > Sent: Saturday, 23 September 2000 2:07 > To: categories@mta.ca > Subject: categories: characterisation of nerve of omega-categories > > > Dear all, > > I don't remember where I could find a characterization for > a simplicial set to be the simplicial nerve of some strict > globular omega-category ? I think that the characterization > is that the simplicial set must be given with a structure > of thin elements satisfying some axioms like the filling of > horners and thin horners. Could you send me a reference please ? > > Thank you in advance. pg. > > > From rrosebru@mta.ca Mon Sep 25 15:52:59 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA25905 for categories-list; Mon, 25 Sep 2000 14:05:42 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200009251257.OAA14220@pandora.cs.kun.nl> X-Mailer: exmh version 2.1.1 10/15/1999 To: categories@mta.ca Subject: categories: PhD & postdoc positions available Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Mon, 25 Sep 2000 14:57:00 +0200 From: Bart Jacobs Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 [Apologies for multiple copies.] Several PhD and postdoc positions are available in the area of formal methods for object-oriented languages, at the University of Nijmegen, The Netherlands. The emphasis lies on using proof tools (esp. PVS) for Java(Card) program verification. More information at the URL: http://www.cs.kun.nl/~bart/LOOP/vacancies.html Best regards, Bart Jacobs. From rrosebru@mta.ca Wed Sep 27 13:34:45 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA22009 for categories-list; Wed, 27 Sep 2000 11:26:30 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 26 Sep 2000 10:30:36 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Tor in toposes Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 27 The category of abelian groups (or modules over a ring object) in a Grothendieck topos does not have any non-zero projectives in general. But free modules are still flat (because the associated sheaf functor preserves sums and monics) and so every module has a flat resolution and this ought to suffice to define Tor. But there are some delicate questions involving well-definedness and functoriality because you cannot lift maps between flats. Does anyone know if this has been published anywhere? From rrosebru@mta.ca Fri Sep 29 16:10:42 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA22255 for categories-list; Fri, 29 Sep 2000 14:16:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 Message-Id: Date: Fri, 29 Sep 2000 17:25:06 +0100 To: wadt2001@disi.unige.it From: WADT 2001 Subject: categories: WADT/CoFI 2001: Call for abstracts Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 WADT/CoFI 2001 15th International Workshop on Algebraic Development Techniques joint with General Workshop of the CoFI WG & CASL Tutorial Genova, Italy 1-3 April 2001 http://www.disi.unige.it/wadt2001/ Aims and Scope ============== The algebraic approach to system specification and development, born as a formal method for abstract data types, encompasses today the formal design of integrated hardware and software systems, new specification frameworks and programming paradigms (such as object-oriented, logic and higher-order functional programming) and a wide range of application areas (including information systems, concurrent and distributed systems). The topics of the workshop include, but are not limited to: - algebraic specification - other approaches to formal specification - specification languages and methods - term rewriting and proof systems - specification development systems (concepts, tools, etc.) The workshop will provide an opportunity to present recent and ongoing work, to meet colleagues, and to discuss new ideas and future trends. The workshop will start with a full day tutorial on CoFI, the Common Framework Initiative for algebraic specification and development of software, see http://www.brics.dk/Projects/CoFI. This tutorial will also be available to people who do not wish to participate in the rest of the workshop. Besides the tutorial, there will be CoFI Task Group meetings and presentation on related topics during the workshop. The workshop will be a satellite event of the European Joint Conferences on Theory and Practice of Software (ETAPS2001). Special deals will be available for participants wishing to attend WADT/CoFI 2001 together with other events of ETAPS. More information on ETAPS is available at http://www.disi.unige.it/etaps2001/ Submissions =========== The scientific programme of the workshop will include up to about 30 presentations of recent results and ongoing research. The presentations will be selected according to originality, significance, and general interest, on the basis of submitted abstracts. The selection committee consists of the WADT Steering Committee together with the local organizers (listed below). The abstracts must be in pdf (or standard postscript) format, up to two pages long in the style for publication in Lecture Notes in Computer Science (see http://www.springer.de/comp/lncs/authors.html), and should be sent by e-mail to wadt2001@disi.unige.it. The deadline for submission of abstracts is 10 January, 2001. Abstracts that substantially depart from the required format, style or length may be rejected without consideration. The final versions of the selected abstracts (due by 26 February) will be made available on the workshop web page, and included in a hand-out for the workshop participants. After the workshop, selected authors will be invited to submit full papers for the refereed proceedings, which is expected to be published as a volume of Springer Lecture Notes in Computer Science (http://www.springer.de/comp/lncs/). Location ======== WADT/CoFI 2001 will be held in Genova. Information are also be available on the web at the page http://www.disi.unige.it/wadt2001/ ********************************************************************** ************************** Important Dates *************************** ********************************************************************** * Deadline for abstracts: 10 January, 2001 * * Notification sent to authors: 26 January, 2001 * * Final abstract due: 26 February, 2001 * * Workshop dates: 1-3 April, 2001 * ********************************************************************** WADT Steering Committee ======================= Michel Bidoit (Cachan, France) Hans-Joerg Kreowski (Bremen, Germany) Peter Mosses, chair (Aarhus, Denmark) Fernando Orejas (Barcelona, Spain) Francesco Parisi-Presicce (Rome, Italy) Donald Sannella (Edinburgh, Scotland) Andrzej Tarlecki (Warsaw, Poland) Sponsors ======== The workshop is organized by IFIP WG1.3 (Foundations of System Specification) jointly with CoFI WG. Local Organizers ================ Maura Cerioli Gianna Reggio DISI Universita' degli Studi di Genova Genova - Italy Email: wadt2001@disi.unige.it ---------------------------------------------------------------------- From rrosebru@mta.ca Fri Sep 29 16:20:24 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA23679 for categories-list; Fri, 29 Sep 2000 14:18:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Tech report: Models for Name-Passing Processes Date: Fri, 29 Sep 2000 15:20:54 +0100 From: Luca Cattani Message-Id: Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 The following paper by Gian Luca Cattani and Peter Sewell Models for Name-Passing Processes: Interleaving and Causal is available as Technical Report 505 of Cambridge University Computer Laboratory electronically from http://www.cl.cam.ac.uk/users/glc25/modnppictr.html or http://www.cl.cam.ac.uk/users/pes20/ or, in hard copy, by emailing "tech-reports@cl.cam.ac.uk". An abstract is attached below. Luca Abstract: We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual pi-calculus operations, defining Indexed Labelled Transition Systems. For non-interleaving causal semantics we define Indexed Labelled Asynchronus Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of name-passing calculi. From rrosebru@mta.ca Fri Sep 29 16:24:07 2000 -0300 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA19051 for categories-list; Fri, 29 Sep 2000 14:25:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <39D4CF8F.387F3237@comlab.ox.ac.uk> Date: Fri, 29 Sep 2000 18:21:19 +0100 From: Samson Abramsky Organization: Oxford University Computing Laboratory, UK X-Mailer: Mozilla 4.75 [en] (X11; U; SunOS 5.7 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: REMINDER: Submission Deadline for TLCA 01 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 32 This is a reminder about the submission deadline for: Fifth International Conference on Typed Lambda-Calculi and Applications which will be held in Krakow, Poland, May 2nd-5th, 2001. The deadline is: OCTOBER 9TH 2000. The scientific scope of TLCA is quite broad, and includes topics from proof theory and semantics to types and logical frameworks, and functional and logic programming. The original call-for-papers follows: (see also the home page at http://www.ii.uj.edu.pl/zpi/tlca2001/) ******************************************************** * * TLCA 2001 * * 5th International Conference on * Typed Lambda Calculi and Applications * May 2 -- 5, 2001 * Krakow, Poland * ******************************************************** * CALL FOR PAPERS ******************************************************** The TLCA series of conferences aims at providing a forum for the presentation and discussion of current research in a field which was originally rather restricted, but has now expanded considerably. Typical areas include, but are not limited to: Proof theory: Natural Deduction and Sequent Calculi, Cut elimination and Normalization, Computational interpretations of Classical Logic, Linear Logic and Proof Nets, Bounded systems capturing complexity classes Semantics: Denotational semantics, Operational semantics, Game semantics, Realizability, Categorical models, Logical Relations, Full Completeness Implementation: Abstract machines, Parallel execution, Optimal Reduction Types: Polymorphism, Dependent types, Intersection types, Subtypes Logical Foundations: Logical Frameworks, Pure Type Systems, Proof checking Programming: Foundational aspects of: Functional programming, Proof search and logic programming, Connections between and combinations of functional and logic programming, Type checking, Higher-order rewriting, Higher-order unification and matching Important Dates =============== Deadline for Submissions: October 9, 2000 Notification to Authors: December 18, 2000 Final Versions due: February 1, 2001 The accepted papers will be published as a volume of the Springer Lecture Notes in Computer Science. Information about LNCS can be found at: http://www.springer.de/comp/lncs/index.html Submission Guidelines ===================== Papers should not exceed 15 standard A4 or US quarto pages, and should allow the Programme Committee to assess the merits of the work: in particular, references and comparisons with related work should be included. Submission of material already published or submitted to other conferences with published proceedings is not allowed. If available, e-mail addresses and fax numbers of the authors should be included. Electronic submissions ====================== Electronic submissions are strongly encouraged. A gzipped Postscript version of the paper should be sent as an e-mail message to: tlca01@comlab.ox.ac.uk In addition, the following information in ASCII format should be sent to this address in a **separate** e-mail: Title; authors; communicating author's name, address, and e-mail address and fax number if available; abstract of paper. Hard-copy submissions ===================== If electronic submission is not possible, authors may submit five (5) hard copies of the paper by post to the following address: TLCA 2001 (Attention: S. Abramsky) Oxford University Computing Laboratory Wolfson Building Parks Road Oxford OX1 3QD United Kingdom Questions concerning submissions ================================ These should be addressed to the Program Chair, Samson Abramsky: samson@dcs.ed.ac.uk Program Committee ================= S. Abramsky (Edinburgh) (chair) P.-L. Curien (Paris) P. Dybjer (Goteborg) T. Ehrhard (Marseille) M. Hasegawa (Kyoto) F. Honsell (Udine) D. Leivant (Bloomington) S. Ronchi della Rocca (Turin) H. Schwichtenberg (Munich) P. Scott (Ottawa) J. Tiuryn (Warsaw) Organizing Committee ==================== M. Zaionc (chair) P. Urzyczyn TLCA 2001 web page ================== http://www.ii.uj.edu.pl/zpi/tlca2001/