March 2010 - Categories - categories.org.au

Research positions
by Maria Manuel Clementino 26 Feb '14

26 Feb '14

5-YEAR RESEARCH POSITIONS The Centre for Mathematics of the University of Coimbra (CMUC) invites applications for five 5-year research positions in all areas of Mathematics. Applicants should have a PhD in Mathematics and at least three years of post-doctoral experience, with an international-level publication record and demonstrated ability to perform independent research. Preference will be given to candidates working in one of the areas in which the members of CMUC are currently active. A very good command of English is required. The appointments will be made for three years, renewable for two more. Successful applicants are expected to develop research within the areas of interest of CMUC. They should also contribute to graduate studies, supervising students from the Department of Mathematics. The basic salary is equivalent to the index 195 of the Portuguese research career (in the order of 42 500 euros a year), in accordance with the Ciência 2008 guidelines http://alfa.fct.mctes.pt/apoios/contratacaodoutorados/edital2008 Benefits include private health insurance and social security. Applicants should send • cover sheet (available from www.mat.uc.pt/cmuc/coversheet.pdf) including names and contact information of three persons who can provide a letter of recommendation • curriculum vitae (publication list included) • a 5-year research proposal (2 pages max), emphasizing their own research goals as pdf files to cmuc(a)mat.uc.pt. The subject of the e-mail message must include the job reference C2008 FCTUC CMUC v15-v19. The deadline for applications is *September 10, 2008.* ------------------------------ More information can be found at www.mat.uc.pt

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separable locale
by Thomas Streicher 17 May '13

17 May '13

Recently rereading Fourman's "Continuous Truth" I came across the term "separable locale" but could nowhere find an explanation. Does it mean a cHa A for which there exists a countable subset B such that ever a in A is the supremum of those b in B with b leq a. This would be the point free account of "second countable", i.e. having a countable basis. Of course, second countable T_) spaces are separable, i.e. have a countable dense set. Is this reading the "usual" one? Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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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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Reminder: MFPS XXVI
by Richard Blute 30 Mar '10

30 Mar '10

This is a reminder of the upcoming event MFPS. In particular, we want to make sure that students and others wishing to apply for support realize they must do so by March 31st. Thanks. The organizers: Richard Blute, rblute(a)uottawa.ca Philip Scott, phil(a)site.uottawa.ca Michael Warren, mwarren(a)uottawa.ca > > > > > > > MFPS XXVI (Mathematical Foundations of Programming Semantics) will > be held at the University of Ottawa, May 6-10 2010 , partially sponsored > by the US Office of Naval Research and the Fields Institute. > > Information on the aims and scope of the conference, as well as invited > speakers, > tutorials and special sessions can be found at: > > http://www.math.tulane.edu/~mfps/mfps26/MFPS_XXVI.html > > The Fields registration webpage is at: > http://www.fields.utoronto.ca/programs/scientific/09-10/MFPS26/ > > Registration and early requests for student support can be done online at > the Fields Institute address above. > > Note: some money is available to partially support graduate students, > postdocs and researchers without grants. Those who wish to apply for this > support should do so right away on the Fields registration page (before > March 31). In your application for support, please state clearly what your > research program is, in what way MFPS is relevant to your research, and > whether you have access to other funds. Priority will be given to students > who do not have access to other funding for travel. > > Graduate students please note: there will be a special student session of > short presentations, and students who wish to apply to speak should also > tell us. > > There is a planned conference banquet, to be announced soon. > > Accommodation: we have reserved rooms in several hotels near campus, as > well as in the university residence. The university residence suites are a > very good deal: a two room suite and kitchen is $90. On the local web > page of the event you will find more information on this. Please note that > in order to take advantage of the discount rate most bookings have to be > done before April. Here is the local web page: > > http://aix1.uottawa.ca/~mwarren/MFPS/index.html > > If you have any questions please do not hesitate to contact one of the > organizers, > > Richard Blute rblute(a)uottawa.ca > Philip Scott phil(a)site.uottawa.ca > Michael Warren mwarren(a)uottawa.ca > > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CFP: Category Theory 2010
by Bob Rosebrugh 30 Mar '10

30 Mar '10

CALL FOR PAPERS The next International Category Theory Conference will take place in Genoa (Italy), from Sunday, 20 June, through Saturday, 26 June, 2010. We look forward to meeting you in Genoa. Contributed talks in all aspects of Category Theory are welcome and we especially encourage submission of work on applications, as well as on foundations. If you would like to give a talk, please submit a title and an abstract of at most *one page* by email (text, or pdf attachment) to: Bob Rosebrugh <rrosebrugh(a)mta.ca> *before May 10* All talks will be held at DIMA-DISI, via Dodecaneso 35, Genova. The conference website at http://ct2010.disi.unige.it/ contains essential information, including travel and accommodation. It will be updated as details become available. Registration will open in mid April. A list of hotels is on the website now. The invited speakers are: Olivia Caramello, Cambridge-Pisa Denis-Charles Cisinski, Paris George Janelidze, Cape Town Andre Joyal, Montreal Matias Menni, La Plata Mark Weber, Paris The Scientific Committee is: Clemens Berger Marta Bunge Maria M. Clementino Robin Cockett Martin Hyland Bill Lawvere Bob Rosebrugh (chair) Ross Street Enrico Vitale Bob Walters The Organizing Committee is Eugenio Moggi Marco Grandis Sandra Mantovani Giuseppe Rosolini (chair) Robert F.C. Walters Best wishes, Bob Rosebrugh, for the CT2010 Committees [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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preprint available
by Anders Kock 30 Mar '10

30 Mar '10

My manuscript "Geometric Algebra of Projective Lines" is available at arXiv, http://arxiv.org/abs/1003.2095 It is a sequel to the preprint on "Abstract Projective Lines" posted in December 2009. Abstract: The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid. (The *multiplication* of the field comes from the *composition* of the groupoid; the crux is to reconstruct the *additive* structure.) Anders Kock [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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"censorship" and categories
by Bob Rosebrugh 29 Mar '10

29 Mar '10

Dear Colleagues, Twenty years ago this month I initiated a mailing list on category theory. During the last two decades there have been many useful exchanges of ideas. Sometimes these have become heated. Eventually a policy on acceptable postings became necessary. That policy is on the web page for the list which is linked at the bottom of every message. It states: "The moderator will not modify articles except for minor typographical and formatting changes. Thus, no offensive or defamatory material should be sent (it will be returned and not posted), and inflammatory posts are discouraged. Nevertheless, wide latitude for vigorous debate is allowed. The categories mailing list distributes *only text* messages. *Do not send attachments, html or excessively long postings* (greater than about 10K). Postings with attachments or ones with html *will be discarded*; long postings may be. Help with avoiding html is here or here." No one has ever objected to the policy, and I have tried to follow it. The policy means that not everything sent to the list will be forwarded. That is the nature of a moderated mailing list. Recently several emails have been circulated to a long list of category theorists, and also sent to the categories list. Some of them have been rejected for forwarding because they do not comply with the policy above. This is regrettable. It is not a pleasure to reject items. I am writing to urge all members of the categories list to read the policy again and to ensure that any message sent to the list has been carefully considered and is acceptable. Using the "reply all" function has sometimes had unintended consequences. In particular, I would like to remind you all that messages containing html are *not* acceptable. Avoiding html is easy and a good idea anyway. Messages of more than a few paragraphs are also not suitable. The web provides many locations, some explicitly devoted to category theory, where longer items may be published. best wishes to all, Bob Rosebrugh [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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link to article
by Ross Street 29 Mar '10

29 Mar '10

Here is a link to my Encyclopedia artice: http://www.maths.mq.edu.au/~street/Encyclopedia.pdf Thank you, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Opposites via distributors
by JeanBenabou 28 Mar '10

28 Mar '10

Dear Ross, I have a little more time to answer your mail. I have to recall precisely what I said about you in my long mail about "opposites via distributors" (i) Ross Street's 1980 paper: Fibrations in bicategories, where he .. uses distributors in the enriched case, which he calls "modules", without mentioning my name. I have again consulted your paper, to be absolutely sure. No mention of my name in the text, but that could be a slip, but no mention of my paper on distibutors, which you knew of course, in the bibliography. The only reference you give about the subject is Lawvere' 1974 paper on "Metric spaces". You say you are saddened, an I'm sorry about that. What about me? Isn't there any reason why I should also be "saddened"? I have carefully looked at the Encyclopedia papers you kindly sent me, and I would like to make a few comments, without any "polemic spirit" About distributors you say, I quote you: " There is a bicategory Mod whose objects are (small) categories and whose arrows are modules [St5, St8] (= profunctors = distributors [Bn2] = bimodules [L2]) What does "There is" mean? Was it "god-given", or introduce by your two papers (1981 & 1983) or Lawvere's paper (1974)? Wouldn't it have been "fairer" and more accurate to say "introduced by Benabou, and used, or developed, or whatever you want, by so and so" Now a few more remarks: In your encyclopedia paper you say: "There are several purely categorical motivations for the development of bicategory theory. The first is to study bicategories following the theory of categories but taking into account the 2-dimensionality; .... A given concept of category theory has several generalizations ... " Sorry Ross, much as I respect your work, we don't seem to have the same approach to generalizations. I introduced bicategories because I had a huge amount of mathematically important examples. And I wanted to have a "common denominator" explaining these examples, and others I was sure to find. And these examples were also a guide to indicate what meaningful "abstract notions" were to be investigated. Let me risk a parallel. Formally, a category is "nothing but" a monoid with many objects. Do you think that Eilenberg & Mac Lane's motivation to introduce categories was " following the theory of monoids" but "taking into account" the fact that they had many objects. If they hadn't had so many mathematical examples would the theory of monoids have indicated them that monos, epis, products, equalizers or general limits or colimits were relevant to the study of "monoids with many objects". Would Kan have discovered adjoint functors if he hadn't had in mind many many important mathematical examples? Even such "formal constructions" on categories e.g. categories of fractions, were motivated by mathematics, not abstract formal considerations. You also mention a coherence theorem asserting that every bicategory is equivalent to a 2-category. About this theorem, or the one stating that every fibration is equivalent to a split fibration, I'm tempted, with all due respect, to say so what? They might be interesting if we were concerned by a single bicategory or fibration. But the natural notion of morphism, in both cases does not respect the "stictness properties". Thus, here again, mathematics, not abstract formalism, will tell me what is really important. I apologize for such a long, and probably a bit confuse mail. Very cordially, Jean. > Dear Jean > > Thank you for forwarding your message to me although I am quite > saddened by it. I have great respect for your work. I have referred > to your work in many places: I attach an encyclopedia article > published by Kluwer in 2000 as an example. Despite what you might > think, I have always tried to use established terminology when it > existed. The move from bimodule (as used by Lawvere in his metric > space paper --- which paper did refer to your Louvain notes) to > module was precisely to make use of the arrow notation and not to > interfere with your use of "bi" as in your word "bicategory". Sammy > had turned me off "distributor" with some remarks at Oberwolfach. > > Best wishes, > Ross > > <Encyclopedia.pdf> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Are there exactly 11 categories with 3 arrows?
by Mark Spezzano 28 Mar '10

28 Mar '10

Hi, This is a beginner's question. I have a textbook (Walters) that asks to show that there are exactly 11 categories with 3 arrows. Now, my logic tells me that I need to cover three possibilities: a) One object with three arrows. How many are there of these? b) Two objects with three arrows. How many are there of these? c) Three objects with three arrows. I think that the answer to this is the easiest. The answer is 1 categories because they are all endomorphisms, each object containing just the identity morphism. So the other 10 arrows must come from a) and b), but I keep getting different answers like 12 and 13 categories as the total. Can someone please explain to me the combinations of categories that need to be covered and why some are missed out during the calculation. Any help would be immensely appreciated. Thanks, Mark Spezzano [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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