2nd Call for Abstracts DOMAINS VI http://www.cs.bham.ac.uk/~wd6/index.html Birmingham, 16-19 September 2002 INTRODUCTION The Workshop on Domains is aimed at computer scientists and mathematicians alike who share an interest in the mathematical foundations of computation. The workshop will focus on domains, their applications and related topics. Previous meetings were held in Darmstadt (94,99), Braunschweig (96), Munich (97) and Siegen (98). FORMAT The emphasis is on the exchange of ideas between participants similar in style to Dagstuhl seminars. In particular, talks on subjects presented at other conferences and workshops are acceptable. INVITED SPEAKERS Ulrich Berger University of Wales Swansea Thierry Coquand Goeteborg University Jimmie Lawson Louisiana State University John Longley University of Edinburgh Dag Normann University of Oslo Prakash Panangaden McGill University Uday Reddy University of Birmingham Thomas Streicher Darmstadt University SCOPE Domain theory has had applications to programming language semantics and logics (lambda-calculus, PCF, LCF), recursion theory (Kleene-Kreisel countable functionals), general topology (injective spaces, function spaces, locally compact spaces, Stone duality), topological algebra (compact Hausdorff semilattices) and analysis (measure, integration, dynamical systems). Moreover, these applications are related - for example, Stone duality gives rise to a logic of observable properties of computational processes. As such, domain theory is highly interdisciplinary. Topics of interaction with domain theory for this workshop include, but are not limited to: program semantics program logics probabilistic computation exact computation over the real numbers lambda calculus games models of sequential computation constructive mathematics recursion theory realizability real analysis topology locale theory metric spaces category theory topos theory type theory SUBMISSION OF ABSTRACTS One-page abstracts should be submitted to domainsvi@cs.bham.ac.uk Shortly after an abstract is submitted (usually one or two weeks), the authors will be notified by the programme committee. The criterion for acceptance is relevance to the meeting. In particular, talks on subjects presented at other conferences and workshops are acceptable. DEADLINE Abstracts will be dealt with on a first-come/first-served basis. We ask potential speakers to express the intention to give a talk as early as possible. REGISTRATION The registration fee will be kept low. Arrangements are not available at this stage. ACCOMODATION We meeting will take place at "The Manor House" halls of residence of the University of Birmingham (http://www.bham.ac.uk/conferences). More details will be provided at a later date. PROGRAMME COMMITTEE Martin Escardo University of Birmingham Achim Jung University of Birmingham Klaus Keimel Darmstadt University Alex Simpson University of Edinburgh ORGANIZATION COMMITTEE Martin Escardo University of Birmingham Achim Jung University of Birmingham PUBLICATION We plan to publish proceedings of the workshop in ENTCS (Elsevier's Electronic Notes in Theoretical Computer Science) series. There will be a call for papers after the workshop takes place. The papers will be refereed according to normal publication standards. URL http://www.cs.bham.ac.uk/~wd6/index.html 9-May-2002 11:35:15 -0300,2507;000000000000-00000000 Return-path: <cat-dist@mta.ca> Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 May 2002 11:35:15 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 3.36 #6) id 175ozv-0003aw-00 for categories-list@mta.ca; Thu, 09 May 2002 11:34:23 -0300 Subject: categories: Re: categories differentiables From: Eduardo Dubuc <edubuc@dm.uba.ar> Date: Wed, 8 May 2002 15:43:25 -0400 (ART) To: categories@mta.ca (categories) In-Reply-To: <200205061851.g46IpGi23281@math-ws-n09.ucr.edu> from "baez@math.ucr.edu" at May 06, 2002 11:51:16 AM X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20020508194333Z435704-32301+1068@mate.dm.uba.ar> Sender: cat-dist@mta.ca Precedence: bulk
Andree C. Ehresmann wrote:
Already in the fifties, Charles Ehresmann has introduced and extensively studied categories internal to Diff (which he called "categories differentiables") in his development of Differential Geometry.
I'm sorry to have not yet gotten ahold of the references you provided - I got distracted by other matters - but if you will forgive my laziness, I'll ask another question:
Could someone please explain how Charles Ehresmann dealt with the fact that Diff does not have all pullbacks? In the definition of internal category we need a pullback to exist: the "object of composable pairs of morphisms", C_1 x_{C_0} C_1. These days, people working on Lie groupoids usually impose some requirements on the source and target maps s,t: C_1 -> C_0 that ensure that this pullback exists. Personally I lean towards a simpler approach, which is simply to demand that the pullback exists. This makes it harder to prove certain theorems, but has a certain charm. I'm wondering what Charles Ehresmann thought about this issue.
Best,
The category Diff has pull-backs of transversal maps, and furthermore these are the only "correct" pull-backs. A natural (and "necessary") requirement for the existence of a given pull-back is transversality, which has a lot of charm. In the well adapted models of SDG all pull-backs of differential manifolds exists, but they will be objects in the topos (actually C-infinity Schemes) which are not differential manifolds unless the pull-back is transversal. The work of Charles Ehresmann and Andre Weil is very much related to this fact. Best, edubuc.