September 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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What else do simplicial sets classify?
by Andrej Bauer 05 Oct '11

05 Oct '11

The presheaf category of simplicial sets is the classifying topos for the theory L of a bounded linear order. In general, there could be other theories which are "Morita equivalent" to L in the sense that their classifying toposes are equivalent to simplicial sets. Are any such known, preferably occurring in nature? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: The omega-functor omega-category
by John Baez 06 Oct '10

06 Oct '10

David Leduc wrote: >> I'm not sure what [_._] is supposed to mean - an internal >> hom functor? > This was supposed to be the "cartesian closed structure" of > StrictOmegaCat, but since some say it is not a structure I'm not sure > how to call it... Just call it the internal hom. The point is, you can just look at a category and say, yes or no, whether it's cartesian closed. So cartesian closedness is a "property" of a category - not a "structure" that you might equip a category with in more than one way. Nonetheless, you can consider properties as a special case of structures - namely, those structures for which you have at most one one choice. And if you do this you're free to speak of a cartesian closed "structure". Similarly, you can consider structures as a special case of "stuff". If you don't know the yoga of "properties, structure and stuff", you might enjoy this paper where Mike Shulman and I explain it: http://arxiv.org/PS_cache/math/pdf/0608/0608420v2.pdf#page=15 Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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EVIL terminology
by Juergen Koslowski 06 Oct '10

06 Oct '10

Dear all, In photo circles EVIL is currently used as an acronym for "Electronic Viewfinder Interchangable Lens" cameras, a new form of cameras that do away with the optical viefinder. Probably this is as firmly toungue-in-cheek as the use of the term "evil" in certain areas of category theory. And while I don't know if many photographers are offended by this term, this obviously is the case with some of our colleagues in category theory. While I'm sure that everybody agrees that the concept as such is important and worth studying, the ongoing dispute over the terminology seems to be rather counterproductive. Of course, one problem with mathematidcal terminology is that so many terms are overloaded by now (natural, continuous...) Any term borrowed from the realm of everyday life will carry certain overtones (and will irritate non-mathematicians). On the other hand, acronyms can come across a clumsy and an impediment to speach (ufl-functors). Maybe it is not too late to find a clever new name for the concept that does convey the negative connotations intended by the original adopters of "evil" without being so offensive to others (we don't want to wait 30 or more years before changing terminology, cf. the 2005/06 discussion concerning "cartesian" and "cocartesian"). Peter Freyd was always very inventive coining new terminology, even though not much of it caught on. Let me start by proposing "equi-unstable" and "precarious" as possible replacements for "evil". -- Juergen -- Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj(a)iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Not invariant but good
by John Baez 01 Oct '10

01 Oct '10

Hi - Thanks for posting. I tried to give a formal definition of "evil for structures" in January, > but nobody > challenged it, endorsed it, or had much of an opinion. I remember liking it, but I don't remember what it was! I can look it up... > In the end, the terminology might be doomed, not because it is offensive, > but because people can't agree on any one meaning. > Or it could be like "natural" - it has a technical meaning, but it also has a penumbra of nontechnical meanings that are very important in mathematics. Best, jb

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Re: Haskell Arrows and internal categories
by Mike Stay 01 Oct '10

01 Oct '10

On Mon, Sep 27, 2010 at 3:50 PM, Mike Stay <metaweta(a)gmail.com> wrote: > I'm trying to understand Arrows in Haskell, > http://www.haskell.org/arrows/index.html > but since I haven't become literate yet, I'm not sure I'm getting > everything right. It looks to me like an Arrow is a monoidal closed > category object in Hask. Is that all there is to it? Hmm. After reading "Freyd is Kleisli, for Arrows", it now looks to me like an Arrow is an enrichment. It consists of a V-profunctor - A:C^op x C -> V, where V is a monoidal category, together with a natural transformation - arr:Hom => A and dinatural transformations - compose:A(b,c) x A(a,b) => A(a,c) - first:A(a,b) => A(a tensor c, b tensor c) satisfying various coherence laws. -- Mike Stay - metaweta(a)gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Grothendieck downloads
by Michael Barr 01 Oct '10

01 Oct '10

Someone asked me how many times it has been downloaded. Finally, I asked our sysop and he just gave me the answer: 1038. Including 41 just in the last five days. I did upload a later version yesterday, but it just fixed a desaccord of number in the opening paragraph of the intro and is not really worth downloading for. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: The omega-functor omega-category
by Tom Leinster 30 Sep '10

30 Sep '10

Dear David, Regarding omegaCat as the terminal coalgebra for ( )-Cat: On Mon, 27 Sep 2010, David Leduc wrote: > Good, good! I am thrilled by such (co)recursive definitions. > In fact was asking about a (co)recursive of the cartesian closed > structure of omegaCat. > Do you have something in store? I'm not aware that anyone has thought particularly about the cartesian closed structure in this context. But being cartesian closed is a *property*, not extra *structure*, and for reasons that Ross explained, it just comes along for the ride. >> As far as I know, this was first observed by Carlos Simpson. > > Any reference? Simpson didn't write it up. However, Eugenia Cheng and I have some related theorems about non-strict omega-categories, which we're currently writing up, and our paper will include an account of Simpson's result. You can read some talk slides on this: see the very bottom of http://cheng.staff.shef.ac.uk/research.html Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: terminology
by Eduardo J. Dubuc 30 Sep '10

30 Sep '10

I appreciate your answer. I appreciate the simple fact that you took time to write me. I never said that my freedom of speech was restricted. I reacted to the spirit of your mail "lets talk about mathematics, lets talk about important things. we are mathematicians, etc etc" I quote: "The longer I have lived the more I have come to suspect solemnity and to see in it - not always but frequently - a cloak for a humbug (Bertrand Russell)" May be I am hypersensitive concerning solemnity. Sorry, e.d. Peter Selinger wrote: > [private reply] > > Eduardo J. Dubuc wrote: >> I do not appreciate that a controversy about terminology be dismissed by >> derision by saying >> >> "thanks for trying to move the discussion away from terminology and back to >> actual mathematical matters". >> >> This kind of solemnity makes me shit !! >> >> No need to move away from terminology, nobody is forbidding you to discuss >> mathematics by discussing terminology, it is not one thing or the other. > > Dear Eduardo, > > Ouch. In fairness, I did not forbid you to discuss terminology. I > simply thanked another person for taking the discussion in another > direction. You have already sent 12 public messages on this subject, > so I don't believe you can fairly claim that your freedom of speech > has been restricted, especially by me. > > Best wishes, -- Peter

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