December 2006 - Categories - categories.org.au

Foundations?
by F W Lawvere 03 Sep '10

03 Sep '10

Down with "Foundations"! Up with algebra! Dear Friends, Presumably I am among those who are being "vilified" as "lovers of categories as foundation". By avoiding any precise definition, such a formulation might appeal to the widespread justified boredom induced by the past hundred years of "foundations as justification". Whenever I used the word "foundation" in my writings over the past forty years, I have explicitly rejected that reactionary use of the term and instead used the definition implicit in the work of my teachers Truesdell and Eilenberg. Namely, an important component of mathematical practice is the careful study of historical and contemporary analysis, geometry, etc. to extract the essential recurring concepts and constructions; making those concepts and constructions (such as homomorphism, functional, adjoint functor, etc.) explicit provides powerful guidance for further unified development of all mathematical subjects, old and new. What is the primary tool for such summing up of the essence of ongoing mathematics? Algebra! Nodal points in the progress of this kind of research occur when, as is the case with the finite number of axioms for the metacategory of categories, all that we know so far can be expressed in a single sort of algebra. I am proud to have participated with Eilenberg, Mac Lane, Freyd, and many others, in bringing about the contemporary awareness of Algebra as Category Theory Had it not been for the century of excessive attention given to the alleged possibility that mathematics is inconsistent, with the accompanying degradation of the F-word, we would still be using it in the sense known to the general public: the search for what is "basic". We, who supposedly know the explicit algebra of homomorphisms, functionals, etc. are long remiss in our duty to find ways to utilize those concepts also in guiding high school calculus. Best wishes, Bill Bibliography: - The Category of Categories as a Foundation for Mathematics, La Jolla conference 1965, Springer (1966) - Adjointness in Foundations, Dialectica, (1969), to be reprinted in TAC - Foundations and Applications: Axiomatization and Education, Bulletin of Symbolic Logic, (2003) vol 9, pp 213-224 - Sets for Mathematics, w/ Bob Rosebrugh, Cambridge Univ. Press, (2003) ************************************************************ 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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groupoids versus homotopy 1-types
by John Baez 05 Jan '07

05 Jan '07

Dear Categorists - The following claim should be well-known (or false), but I don't know a reference: Let Gpd be the 2-category consisting of groupoids functors natural transformations and let 1Type be the 2-category consisting of homotopy 1-types continuous maps homotopy classes of homotopies where for present purposes "homotopy 1-types" means "CW complexes with vanishing higher homotopy groups regardless of the choice of basepoint". Claim: Gpd and 1Type are equivalent (or "biequivalent", in older terminology). In fact I bet there is an explicit pseudo-adjunction between them, with the "fundamental groupoid" 2-functor going one way and the "Eilenberg-Mac Lane space" 2-functor going the other way. Does anyone know for sure? Know a reference? Best, jb

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What is needed for an online journal
by Bill Rowan 03 Jan '07

03 Jan '07

Hello, We have the arxiv preprint server, and other preprint servers. Why is this not sufficient? Because the papers are not refereed and subject to being made better through the work of editors (not that they always improve things). What about having an editorial board, which would look at papers on the arxiv, say, have them reviewed and revised, and then put them back on the arxiv in final form, and listed elsewhere as having been through that process and "blessed" so to speak by the editorial board? What we would all like to have is more prestige for having our papers blessed, and hopefully, read by somebody. In this proposal, the quality of the editorial board's work and the usability of its published listings would be the most important thing. They could even give a negative recommendation for someone's paper, although authors might hope for the opportunity to withdraw their paper if they didn't appreciate the final recommendation. The pulbished listings could include more information than just an up- or down- recommendation to read the paper, it could include comments by other mathematicians. Bill Rowan

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Re: [Nut-upsuser] Re: Re: Newpoint 200897 UPS
by Arjen de Korte 31 Dec '06

31 Dec '06

> Good. So now you should observe how this state changes in response to > power events (lose power, on battery, low battery, battery charging, > etc). If enough of the above flags change in a predictable way, we can > use this to set the ups.status register, which will be enough to drive > upsmon. In fact, that's the only thing upsmon ever looks at. Regards, Arjen -- Eindhoven - The Netherlands Key fingerprint - 66 4E 03 2C 9D B5 CB 9B 7A FE 7E C1 EE 88 BC 57 _______________________________________________ Nut-upsuser mailing list Nut-upsuser(a)lists.alioth.debian.org http://lists.alioth.debian.org/mailman/listinfo/nut-upsuser

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Announcement of Fields Workshop on Traced Monoidal Cats
by Phil Scott 31 Dec '06

31 Dec '06

Dear Colleagues: We would like to announce the following: ============================================================== A Fields Institute Sponsored Workshop Recent advances in category theory and logic: Applications of traces to algebra, analysis and categorical logic University of Ottawa April 28-30, 2007 +++++++++++++++++++++++++++++++++++++++++++++++ The abstract theory of traces has had a fundamental impact on a variety of fields within mathematics. These range from functional analysis and noncommutative geometry to topology and knot theory, and more recently to logic and theoretical computer science. The theory of traced monoidal categories, due to Joyal, Street and Verity, is an attempt to unify various notions of trace that occur in these diverse branches of mathematics. More recent developments include several theories of partial traces in monoidal categories. The Logic and Foundations of Computing Group at the University of Ottawa, with funding from the Fields Institute, is proud to host a workshop to explore these topics. The purpose of this workshop is to bring together researchers in these fields to look for common developments, models, and applications of trace theory. Among the applications are various notions of parametrized traces arising in operator algebras, in the theory of feedback and recursion in theoretical computer science, in braid closure in knot theory, and in dynamics of proofs as expressed by Linear Logic and the Geometry of Interaction. Some invited speakers include: Samson Abramsky (Oxford) Robin Cockett (Calgary) Andre Joyal (UQAM) Louis Kauffman (Illinois) Mathias Neufang (Carleton) We will be announcing further speakers shortly. This is intended to be a workshop, with student participation in mind, including introductory lectures. We will have some funding for student travel and accommodation. Students interested in receiving financial aid should contact the organizers by January 30th. Anyone interested in attending or contributing a talk should contact us by the same date. There will soon be an official webpage. We hope to see you there. The organizers: Phil Scott (phil(a)site.uottawa.ca) Rick Blute (rblute(a)uottawa.ca) Pieter Hofstra (hofstrap(a)cpsc.ucalgary.ca)

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Elsevier
by John Baez 29 Dec '06

29 Dec '06

Jim Stasheff wrote: >One of Elsevier's motives (and other publishers) is close to >trying to corner the market >or at least squeeze out all the profit possible > >we now have several ways to resist >1. choice of journal to which we submit papers >B. choice of journal for which we will perform slave labor (editing) >III. advice in re the above to our mentees I quit serving as an editor for Advances in Mathematics when it was bought by Elsevier. When I learned how bad the situation was, I also quit refereeing for all Elsevier-run journals. People can read the rest of my rant here: http://math.ucr.edu/home/baez/journals.html Best, jb

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Correct address of the NUMDAM site for Cahiers
by Andree Ehresmann 28 Dec '06

28 Dec '06

In my preceding msg, I have given the address of the site where the 7 first volumes of the "Cahiers" are posted (under the heading "Seminaire Ehresmann"). However I have made a slight error (kindly indicated to me by Marco Grandis). The correct address is: http://www.numdam.org/numdam-bin/feuilleter?j=SE&sl=0 With all my best wishes to all Andree C. Ehresmann

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Equitable Mathematics
by joyal.andre＠uqam.ca 24 Dec '06

24 Dec '06

Mike Barr is raising up an important point. We should look at the problem from an economical point of view. The true buyers of scientific journals are the university librairies, not the scientists. There is a demand for low-price-high-quality scientific journals. The mathematical community is the producer. The publisher is the intermediate. The prices are artificially high. We may need an organisation of Equitable Mathematics. The organisation should be supported financially by the university librairies and the mathematical associations. The editorial board of Topology has resigned to protest the price of the journal. I admire their political gesture but unfortunately, it has a drawback: a prestigious journal has disappeared. I have a crazy idea: Topology could be resurrected as a cloned called Equitable Topology. The new journal could have the same editorial board as late Topology, if the editors agree. Other expensive mathematical journals could be duplicated with an Equitable clone having the same editorial board. I am aware of the organisational difficulties of realising the idea of Equitable Mathematics. To be successful, it will have to be done very seriously. It should be economically sound. Maybe the mathematical associations should be involved in the organisation. Andre ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.

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CT2007 - second announcement
by Category Theory 2007 22 Dec '06

22 Dec '06

Please circulate to all interested colleagues. ==================== CT2007 ==================== International Category Theory Conference Hotel Tivoli Almansor Carvoeiro, Portugal June 17-23, 2007 Information about registration, accommodation, travel, abstract submission and deadlines is now available at the web page http://www.mat.uc.pt/~categ/ct2007 Invited Speakers: ----------------------- Dominique Bourn (Calais, France) Marcelo Fiore (Cambridge, UK) Marino Gran (Calais, France) Dirk Hofmann (Aveiro, Portugal) Martin Hyland (Cambridge, UK) André Joyal (Montréal, Canada) F. William Lawvere (Buffalo, USA) Jirí Rosicky (Brno, Czech Republic) Scientific Committee: ---------------------------- Samson Abramsky (Oxford, UK) Jirí Adámek (Braunschweig, Germany) Francis Borceux (Louvain, Belgium) George Janelidze (Cape Town, South Africa) Steven Lack (Sydney, Australia) Michael Makkai (Montreal, Canada) Manuela Sobral (Coimbra, Portugal) Ross Street (Sydney, Australia) Walter Tholen (Toronto, Canada) Organizing Committee: ------------------------------- Diana Rodelo, University of Algarve (drodelo(a)ualg.pt) Manuela Sobral, University of Coimbra (sobral(a)mat.uc.pt) Maria Manuel Clementino, University of Coimbra (mmc(a)mat.uc.pt) Jorge Picado, University of Coimbra (picado(a)mat.uc.pt) Lurdes Sousa, IPViseu (sousa(a)infante.ipv.pt) Maria João Ferreira, University of Coimbra (mjrf(a)mat.uc.pt) Gonçalo Gutierres, University of Coimbra (ggutc(a)mat.uc.pt)

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conference announcement
by Jerome Scherer 20 Dec '06

20 Dec '06

First announcement SECA4, "seminar on Category theory and applications" Barcelona (CRM): June 6 - 9, 2007. This is the fourth conference of a series of meetings held in Spain. It is intended as meeting point for specialists in category theory and related areas as homological algebra, representation theory, or homotopy theory. It is sponsored by the Spanish Ministry of Education, the Catalan Government, and the Centre de Recerca Matematica in Barcelona. Speakers: Denis-Charles Cisinski, Universite Paris 13 Jose L. García Hernandez, Universidad de Murcia Joachim Kock, Universitat Autonoma de Barcelona Henning Krause, Universitaet Paderborn Tom Leinster, University of Glasgow Javier Majadas, Universidade de Santiago de Compostela Ieke Moerdijk, Universiteit Utrecht Antonio Viruel, Universidad de Malaga Survey Talks: Ronnie Brown, University of Wales Carles Casacuberta, Universitat de Barcelona Marco Grandis, Universita de Genova You will find more information on the following webpage http://mat.uab.es/~seca4/ There will be financial support available for young participants. More details will appear in the subsequent announcements. If you have specific questions, please send an email to: seca4(a)mat.uab.es Organizing committee: Pere Ara, Universitat Autonoma de Barcelona Carles Broto, Universitat Autonoma de Barcelona (coordinator) Jose Manuel Casas, Universidad de Vigo Luis Javier Hernandez, Universidad de La Rioja Manuel Ladra, Universidad de Santiago de Compostela Albert Ruiz, Universitat Autonoma de Barcelona Jerome Scherer, Universitat Autonoma de Barcelona Scientific committee: Ronnie Brown, University of Wales Carles Casacuberta, Universitat de Barcelona Jose Luis Gomez Pardo, Universidad de Santiago de Compostela Marco Grandis, Universita di Genova Lionel Schwartz, Universite Paris 13

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