August 2003 - Categories - categories.org.au

Uniform spaces
by Tom Leinster 03 Sep '03

03 Sep '03

Hello, Does anyone know of any account of the basic properties of the category of uniform spaces? I'm after things like (co)limits, cartesian closure, and (co)limit-preservation by the forgetful functor to Top. Bourbaki gets me some of the way, but his decision not to use categorical language and the resulting circumlocutions make it a struggle. Thanks, Tom

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Please send message again
by F W Lawvere 30 Aug '03

30 Aug '03

[Note from Moderator: several list-members have noted that spurious messages have portrayed them falsely as sender. We all hope that the current internet mess will be resolved. Patience may be necessary. In the meantime, Bill's message indicates a probably non-unique situation that we should also all be aware of. best wishes, Bob] Dear friends, In case you have not received an answer to any message you may have sent to me during the last few weeks of the virus attack, please send your message again. I have the impression that some genuine messages may have been lost along with the hundreds of spurious ones. Bill Lawvere ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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Category Theory and Computer Science, TAC Special Volume
by Rick Blute at 28 Aug '03

28 Aug '03

SPECIAL VOLUME OF THEORY AND APPLICATIONS OF CATEGORIES (TAC) Proceedings, Category Theory and Computer Science CTCS'02 Guest Editors - Rick Blute(Ottawa) and Richard Wood (Dalhousie) Call for Papers http://www.tac.mta.ca/tac/ This special volume of Theory and Applications of Categories is devoted to the proceedings of the 2002 conference Category Theory and Computer Science, held at the University of Ottawa. The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory. Indeed, category theory provides one of the key tools in the analysis of the interaction between logic and the theory of computation. The extent to which category theory has influenced these areas can be seen from the following list of topics, which are typical of the interests of this conference: -coalgebras and computing -concurrent and distributed systems -constructive mathematics -declarative programming and term rewriting -domain theory and topology -foundations of computer security -linear logic -modal and temporal logics -models of computation -program logics, data refinement, and specification -programming language semantics -type theory The list is by no means exhaustive. This special volume is devoted not just to journal versions of the papers which appeared in the proceedings, but is intended to showcase papers which emphasize any of the above topics. Papers will be refereed to the usual high standards of TAC. * Submission deadline: January 2nd, 2004. * Submissions, in pdf or ps format, should be sent to Rick Blute at <rblute@mathstat@.uottawa.ca>. * Questions (e.g., about the appropriateness of a submission) and comments should be directed to the same address. * To expedite handling, authors should prepare their manuscripts following the instructions for contributors described in <http://www.tac.mta.ca/tac/authinfo.html>

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Senior Informatics Systems Analyst Positions (2) (fwd)
by M. Healy 28 Aug '03

28 Aug '03

I realize categories is not a bulletin board for employment ads, but I thought some reader of the list might find this one to be of interest. I checked out the firm---Korn/Ferry International. Through their FutureStep subsidiary, they are an executive search firm. Does this mean category theorists have made it into the executive ranks?(!) Mike ---------- Forwarded message ---------- Date: Wed, 27 Aug 2003 00:16:43 -0700 From: Futurestep <owilson.futurestep(a)sbcglobal.net> To: Owen Wilson <owilson.futurestep(a)sbcglobal.net> Subject: Senior Informatics Systems Analyst Positions (2) Based on your interest in Category Theory, I hope you can help me recruit a mathematician. We are seeking two Ph.D. level individuals, one with expertise in CATEGORY THEORY and one with expertise in DISCRETE EVENT MODELING to join a team of 15 top flight biotech industry mathematical modelers. If you have either colleagues or previous students who have such expertise, who you think may be interested, and who also fit in with the requirements listed below, I would very much appreciate hearing back from you -- or you could simply forward this email to the appropriate individual. Owen Wilson, Ph.D. Korn-Ferry/Futurestep Tel: (713) 526-1143 Email: owilson.futurestep(a)sbcglobal.net POSITION DESCRIPTION The group is looking for a few special individuals who can successfully develop innovative applied mathematics solutions to real-world biology, chemistry, applied physics, engineering or operations research problems and translate them into working prototype computer codes. The goal is to use sophisticated mathematics to solve practical problems and to have a significant impact on the success of this biotech company. A PhD in engineering, mathematics, computer science or a physical science is preferred; if mathematics or computer science, significant experience with physical science problems is required. Industry experience is extremely desirable. Candidates with an MS may be considered if there is extensive industrial experience. The successful candidates will develop advanced data analysis techniques, mathematical models and simulators to help optimize performance, increase efficiency, or carry out failure mode analyses on systems in diverse areas such as process development, drug R&D, and manufacturing. Potential applications include, but are not limited to: lumped and distributed parameter (ODE or PDE) continuous simulations; finite-state or petri-based discrete simulations; Monte-Carlo stochastic simulations; nonlinear parameter estimation, Bayesian estimation and error-in-variable models; and digital signal processing, including Fourier and wavelet analyses, filtering and smoothing. Good programming skills are important and object-oriented programming is desirable, as is familiarity with the design and query of relational databases. Experience with software engineering and related tools such as Rational Rose or Erwin is desirable. It is important to be able to understand the underlying architecture of a software system and to be comfortable developing such architectures. Good team skills and the ability to learn quickly are essential. Good oral and written communication skills are important. Frequent formal presentations will be required and formal reports documenting concepts and the delivered proof-of-principle software must be written. A strong ability to communicate results to those who are neither comfortable nor familiar with mathematical terminology is necessary.

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Re: Pat Donaly
by Andree Ehresmann 28 Aug '03

28 Aug '03

In answer to Pat Donaly The notion that Pat proposes has been defined under the name of "U-dominated category" (categorie U-dominee) par Charles Ehresmann in the early sixties (before the notion of an enriched category was introduced), and he has extensively used it in several of his papers during these years ; later he rallied the stricter notion of enrichment. Most of these papers are re-printed in. "Charles Ehresmann : Oeuvres completes et commentees" Part III-2. The definition, introduced in 1963 (cf. p. 492), is also briefly recalled in his book "Categories et Structures" (Dunod 1965, p. 81). An interesting application is given in the (not easy to read) paper "Cohomologie a valeurs dans une categorie dominee" (1966) which contains a lot of ideas which have not been developed later on but would certainly lead to interesting results. In this same volume of the "Oeuvres" I have given a comparison between dominated categories and enriched categories (Comment 699.1 page 829). Andree C. Ehresmann

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module for a category
by Paul B Levy 28 Aug '03

28 Aug '03

Hi Is there a standard reference for the notion of "left module for a category"? (or right module, or bimodule) Is there any reference in the setting of ordinary categories rather than (or as well as) enriched categories or bicategories? Thanks Paul

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Re: E-worms and e-viruses
by David B. Benson 27 Aug '03

27 Aug '03

> I think that most net users are by now pretty much aware that spoofing is very common... Fine, David -- Professor David B. Benson (509) 335-2706 School of EE and Computer Science (EME 102) (509) 335-3818 fax PO Box 642752, Washington State University office: Sloan 308 and 307 Pullman WA 99164-2752 U.S.A. dbenson(a)eecs.wsu.edu ----------------------------------------------------------------------------------

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Special volume of TAC -- reminder
by rjwood＠mathstat.dal.ca 24 Aug '03

24 Aug '03

TAC Special Volume, Reminder of Call For Papers Dear Colleagues Among the many important events which occurred in 2002 was the 60th birthday of Aurelio Carboni. With the approval of the Editorial Board of Theory and Applications of Categories, we wish to honour our friend and colleague Aurelio with a special issue of TAC. Following the editorial policy of TAC, we welcome papers that significantly advance the study of categorical algebra or methods, or that make significant new contributions to mathematical science using categorical methods. Authors are invited to submit their manuscripts in electronic form to any of the Guest Editors no later than December 31, 2003; articles will appear as soon as they are accepted. Authors are asked to prepare their manuscripts following the author information described at http://www.tac.mta.ca/tac/authinfo.html All papers will be carefully refereed following the standards of Theory and Applications of Categories. Guest Editors: George Janelidze george_janelidze(a)hotmail.com Steve Lack stevel(a)maths.usyd.edu.au Bill Lawvere wlawvere(a)buffalo.edu Enrico Vitale vitale(a)math.ucl.ac.be Richard Wood rjwood(a)mathstat.dal.ca

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A remark related to Paul Levy's email on modules (Pat Donaly)
by Jpdonaly＠aol.com 23 Aug '03

23 Aug '03

All categorists: I can't respond to Paul Levy's request for sources, but the issue of categorical modules may relate to a general question regarding the necessity of V-enrichment via monoidal categories. So, in a backhanded sense, it could bear on Paul's apparent search for something independent of standard V-enrichment. Please pardon my naivete---my whole concern with this issue began just a few weeks ago during some correspondence with Gabi Lukacs. First, the connection, then the question: Since I am a little out of sympathy with monoidal categories, if I want to enrich the homsets of a category R into objects of some other category C which has a function-valued forgetful functor U on it, I look for a bifunctor r:RxR'--->C (where R' is the opposite category of R) for which the function composite functor U o r is the identity adjunction on R. This adjunction is the bicomposition functor which sends a pair (a,b) to the function z-->azb (which maps between the obvious homsets). If s:SxS'--->C is another such C-enrichment or structure, then a C-structure morphism from r to s is a functor from R to S which satisfies a certain property which is stated in terms of the identity adjunctions which are at issue. It frequently happens that C has a salient C-structure c:CxC'--->C of its own, in which case I am inclined to call a C-structure morphism from r to c an r-module. Take R to be the multiplicative monoid of a small ring, r to be simultaneous left and right multiplication in R and C to be the category of small commutative group homomorphisms to see that a ring is a C-structure and that an r-module is the usual idea of an R-module in this case. I hope that this is what Paul's question is about. I would like to see more information along these lines, myself. My question generally asks for the relationship between what is apparently called V-enrichment and the idea just outlined. I can see that, if I fix an R'-object in the right argument of a C-structure r, I get an r-module (a left regular r-module, in fact), and, by taking left or co- adjoint functors of such modules (if possible), I should get a tensor product concept which should define a monoidal category composition for which the V-enrichment is r. The literature has presumably examined the extent to which this is valid, and I would appreciate being told where. Second, with my ingrained if idiosyncratic prejudices against monoidal categories, I am curious to know if in some impressive sense all (presumably closed?) monoidal categories come about in this way? Are those which don't particularly interesting? Or is the situation the reverse: Every worthwhile monoidal category comes from a C-structure r, but there are important r's which don't provide a monoidal category. Is the full story laid out in a book? Michael Kelley's book is out of print according to Gabi Lukacs. Any help? Pat Donaly

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Union College Conference -- 2nd Announcement
by Susan Niefield 22 Aug '03

22 Aug '03

This is the second announcement of the Union College Mathematics Conference. The conference will take place November 8-9, 2003 at Union College in Schenectady, NY. There will be plenary talks and parallel sessions for contributed talks in algebraic topology, category theory, and differential geometry. For more information about the conference, including registration, submission of abstracts, housing and transportation, please visit our website at: http://www.math.union.edu/~leshk/03Conference/ The deadline for submission of abstracts is October 17th, and for registration is October 24th. We hope to see you in November! ORGANIZERS Category Theory Susan Niefield niefiels(a)union.edu Kimmo Rosenthal rosenthk(a)union.edu Algebraic Topology Brenda Johnson johnsonb(a)union.edu Kathryn Lesh leshk(a)union.edu Differential Geometry Christina Tonnesen-Friedman tonnesec(a)union.edu

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