August 2014 - Categories - categories.org.au

Partial functor
by David Leduc 17 Mar '15

17 Mar '15

Hi, A partial functor from C to D is given by a subcategory S of C and a functor from S to D. What is the appropriate notion of natural transformation between partial functors that would allow to turn small categories, partial functors and those "natural transformations" into a bicategory? The difficulty is that two partial functors from C to D might not have the same definition domain. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos ...
by Vasili I. Galchin 04 Sep '14

04 Sep '14

Dear Cat People ... I have been re-reading William Lawvere's description of "variable sets" (a functor category) in "a elementary topoi" on a discrete poset/preset vs a "abstract sets" in the topos of abstract sets . In Haskell( and other FPLs .. ) aren't "pure" computations just over the topos of abstract sets and "mutable" /"time-varying/stateful" computations aren't just "variable sets" (i.e. a functor over a discrete preset-poset)?? Please forgive my germ of an idea Kind regards, Vasya P.S. Yes I am familiar with Eugenio Moggi's papers on using monads for stateful computations .. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Uniform locales in Shv(X)
by Jeff Egger 30 Aug '14

30 Aug '14

Dear Simon, I was always told that one of the advantages of the "Tukey-style" definition (in terms of uniform covers) was that it would be easier to generalise toposes than the definition in terms of entourages. And yet, my (admittedly cursory) search for this promised generalisation hasn't turned up anything yet. On the other hand, looking at the work of Jorge Picado et al., it seems to me---and here, I think, you and I are in agreement---that the only axiom which poses any problem is the "admissibility axiom". Specifically, for any locale L (internal to any topos E), one can define an object of Weil entourages for L: it comprises those elements of the frame underlying LxL such that (the nucleus corresponding to) the corresponding open sublocale contains (the nucleus corresponding to) the diagonal sublocale. It is moreover clear that this object is a meet-semilattice, so it makes sense to speak of filters in it---i.e., upward-closed sub-meet-semilattices. A Weil uniformity is a filter in this sense satisfying three further axioms: square-refinement (which asserts that a certain endomorphism of the filter is epi), symmetry (which says the filter is also closed under a further unary operation), and the one problematic axiom, "admissibility"; but I wonder how important this axiom really is? For locales with enough points, it exists to ensure that the topology derived from the uniformity is not coarser than the original. Perhaps, if we define a Weil pseudo-uniformity on L to be exactly as above minus the admissibility axiom, it is possible---at least in the case of a localic topos E=Shv(X)---to describe a second locale underlying the pseudouniformity? If so, then we don't really need formulate the admissibility axiom in the internal language of the topos. Cheers, Jeff. -------------------------------------------- On Thu, 8/21/14, henry(a)phare.normalesup.org <henry(a)phare.normalesup.org> wrote: Subject: Re: categories: Uniform locales in Shv(X) To: "Jeff Egger" <jeffegger(a)yahoo.ca> Cc: categories(a)mta.ca Received: Thursday, August 21, 2014, 7:51 AM Dear Jeff, I think the problem is that (as far as I know) no one has developed a nice constructive theory of uniform locale. If I'm mistaken about that I would be really happy to know more about it. I have done in my thesis (in chapitre 3 section 3, https://www.imj-prg.fr/~simon.henry/Thesis.pdf) the case of constructive metric locale, under the assumption that the map $Y \rightarrow X$ is open. Removing this openness hypothesis seems difficult but I stil have hope that this is possible, and I have a few idea about it... For the general case it seems to me that the only definition that have a chance to work properly without the openess condition is the definition by entourage and this one should be easy to externalise: any local section of the sheaf of entourage will corresponds to an open sublocale of Y \times_X Y, (containing the restriction of the diagonal to the open sublocale of $X$ on which it is defined ), and it should not be to hard to give the axioms that these have to satisfy... is this the kind of things your are looking for ? Best wishes, Simon Henry [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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celebration of Jim Lambek
by Michael Lambek 29 Aug '14

29 Aug '14

Jim Lambek?s family invites you to a celebration of his life Joachim Lambek (December 5, 1922 - June 23, 2014) Saturday, September 20, 2014 12 noon ? 2:00 p.m. Birks Heritage Chapel 3520 University Street Montreal, Quebec H3A 2A7 Tel: 514-398-4121 For parking please see: http://www.mcgill.ca/transport/parking/downtown/wedding-parking Followed by a reception hosted by the Department of Mathematics West Room, Victoria College 2:00 ? 5:00 p.m. Please attend and circulate this invitation to others who may be interested. We also announce the Jim Lambek Prize in Mathematics to be given annually to an outstanding mathematics student at McGill with an interest in linguistics, algebra, logic, or history and philosophy of mathematics. Should you wish to contribute you may do so in one of 4 ways: --online: www.mcgill.ca/give - indicate "Jim Lambek Prize in Mathematics" in the text box for area of donation --by phone: 1-800-567-5175; or at 514 398-5000 --by mail: send a cheque, payable to "McGill University," with "Jim Lambek Prize in Mathematics" in the memo line to: Donation and Record Services McGill University 1555 Peel Street, 9th Floor Montreal, Quebec H3A 3L8 --by means of a pledge card that will be available at the memorial [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Grigori (Grisha) Mints
by Valeria de Paiva 26 Aug '14

26 Aug '14

Dear colleagues, I've checked the archives of categories and it seems that the sad news that Grisha Mints passed away on 29 May 2014 has not reached the community. I am sad to be the bearer of these news. Richard Zach has a nice post about him ( http://www.ucalgary.ca/rzach/blog/2014/05/grigori-mints-1939-2014.html) Stanford has a memorial page ( https://philosophy.stanford.edu/content/articles/view/Grisha_Mints_1/) and his family has a webpage for tributes (http://www.grishamints.net/) I am missing Grisha very much, a great logician and a great human being. Valeria -- Valeria de Paiva http://www.cs.bham.ac.uk/~vdp/ http://valeriadepaiva.org/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Memorial for Jim Lambek 20 Sept 2014
by Robert Seely 26 Aug '14

26 Aug '14

[Apologies to anyone who received duplicate copies of this notice!] (The following message is being sent on behalf of Jim's family:) Friends and collegues of Prof Joachim (Jim) Lambek might want to know that there will be a memorial for Jim on Saturday, September 20, at noon, in the Birks Heritage Chapel on University Street (McGill campus), with a reception to follow at the West Room in Victoria College, also on the McGill campus. In addition, messages and condolences may be added to the following "guest book": http://www.legacy.com/guestbooks/montrealgazette/joachim-lambek-condolences… -- <rags(a)math.mcgill.ca> <www.math.mcgill.ca/rags> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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V-Cat, V-Prof as symmetric monoidal bicategories
by Jamie Vicary 22 Aug '14

22 Aug '14

Hi, Is there a reference that gives the full symmetric monoidal bicategory structure on V-Cat and V-Prof, and which shows that the embedding functor V-Cat-->V-Prof is symmetric monoidal? Cheers, Jamie [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Uniform locales in Shv(X)
by Jeff Egger 22 Aug '14

22 Aug '14

Dear all, I found myself wondering yesterday "what does a uniform locale internal to Shv(X) look like?". In theory, this ought to be quite a simple thing: a locale map Y-->X equipped with a "fibrewise uniform structure". Has anyone already worked out a precise definition for the latter phrase? Pointers to relevant literature would be greatly appreciated! Cheers, Jeff. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Postdoc Position on Verification of Asynchronously Communicating Systems, Inria/LIG, Grenoble, France
by Gwen.Salaun＠inria.fr 19 Aug '14

19 Aug '14

The Convecs team (Inria Grenoble Rh?ne-Alpes research center / LIG laboratory) recruits a postdoc. More information at: http://convecs.inria.fr/jobs/2014b.html Applications should be addressed directly to Gwen Sala?n, preferably by e-mail. Applications received after October 10th, 2014 might not be considered if a candidate has been selected already. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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postdoc grants in Portugal
by Maria Manuel Clementino 19 Aug '14

19 Aug '14

Our national Foundation for Sciences and Technology http://www.fct.pt/index.phtml.en accepts applications for postdoctoral grants until September 30, 2014: http://www.fct.pt/apoios/bolsas/concursos/individuais2014.phtml.en The Regulations can be found at http://www.fct.pt/apoios/bolsas/regulamento.phtml.pt [in Portuguese]. In order to apply the candidate needs the support of a supervisor, working in a Portuguese university. If you're interested, please send me an email. Maria Manuel Clementino <mmc(a)mat.uc.pt> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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