June 2011 - 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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size_question
by Eduardo Dubuc 04 Jul '11

04 Jul '11

This is a naive question on non naive foundations. Consider the inclusion S_f C S of finite sets in sets. Is the category S_f closed under finite limits and at the same time small ? For example, there are a proper class of singletons, all finite. Thus a proper class of empty limits. Question, which is the small category of finite sets ?, which are its objects ?. A small site with finite limits for a topos would not be closed under finite limits ? etc etc But, more basic is the question above: How do you define the small category of finite sets ? Or only there are many small categories of finite sets ? You can not define a finite limit as being any universal cone because then you get a large category. Then how do you determine a small category with finite limits without choosing (vade retro !!) some of them. And if you choose, which ones ? The esqueleton is small but a different question !! e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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aiml 2012 early call for papers
by Silvio Ghilardi 01 Jul '11

01 Jul '11

[Apologize for multiple copies] AiML-2012: FIRST CALL FOR PAPERS 9-TH INTERNATIONAL CONFERENCE ON ADVANCES IN MODAL LOGIC COPENHAGEN, 22-25 AUGUST, 2012 hylocore.ruc.dk/aiml2012 Advances in Modal Logic is an initiative aimed at presenting the state of the art in modal logic and its various applications. The initiative consists of a conference series together with volumes based on the conferences. Information about the AiML series can be obtained at http://www.aiml.net. AiML-2012 is the ninth conference in the series. TOPICS We invite submission on all aspects of modal logic, including: - history of modal logic - philosophy of modal logic - applications of modal logic - computational aspects of modal logic + complexity and decidability of modal and temporal logics + modal and temporal logic programming + model checking + model generation + theorem proving for modal logics - theoretical aspects of modal logic + algebraic and categorical perspectives on modal logic + coalgebraic modal logic + completeness and canonicity + correspondence and duality theory + many-dimensional modal logics + modal fixed point logics + model theory of modal logic + proof theory of modal logic - specific instances and variations of modal logic + description logics + modal logics over non-boolean bases + dynamic logics and other process logics + epistemic and deontic logics + modal logics for agent-based systems + modal logic and game theory + modal logic and grammar formalisms + provability and interpretability logics + spatial and temporal logics + hybrid logic + intuitionistic logic + substructural logics + computationally light fragments of all such logics Papers on related subjects will also be considered. INVITED SPEAKERS: TO BE ANNOUNCED PAPER SUBMISSIONS There will be two types of submissions to AiML-2012 (1) Full papers for publication in the proceedings and presentation at the conference. (2) Abstracts for short presentation only. Both types of papers should be submitted electronically using the EasyChair submission page at http://www.easychair.org/conferences/?conf=aiml2012 (1) FULL PAPERS Authors are invited to submit, for presentation at the conference and publication in the proceedings, full papers reporting on original research and not submitted elsewhere. The proceedings of AiML'2012 will be published by College Publications http://www.collegepublications.co.uk in a volume to be made available at the conference. The submissions should be at most 15 pages, with an optional technical appendix of up to 5 pages, together with a plain-text abstract of 100-200 words. The submissions must be typeset in LaTex, using a style file and template that will be provided on the AiML'2012 website hylocore.ruc.dk/aiml2012. (2) ABSTRACTS These should be at most 5 pages. They may describe preliminary results, work in progress etc., and will be subject to light reviewing. The accepted abstracts will be made available at the conference, and the authors will have the opportunity to make short presentations (of up to 15 minutes) on them. At least one author of each accepted paper or abstract must register for, and attend, the conference to present his or her work. SPECIAL SESSION ON HYBRID LOGIC: Hybrid logic is an extension of modal logic which allows us to refer explicitly to states of the model in the syntax of formulas. There will be a special session of AiML devoted to papers on hybrid logic. The scope of the special session is standard hybrid-logical machinery like nominals, satisfaction operators, and the downarrow binder, but also other extensions of modal logic can be considered.Papers for this session should be submitted the same way as others. PROGRAMME COMMITTEE: Carlos Areces (FaMAF, Universitad Nacional de Cordoba, Argentina) Philippe Balbiani (IRIT, Toulouse, France) Lev Beklemishev (Moscow State University, Russia) Guram Bezhanishvili (New Mexico State University, USA) Nick Bezhanishvili (Imperial College London, UK) Patrick Blackburn (Roskilde University, Denmark) Thomas Bolander (Technical University of Denmark) Torben Brauner (Roskilde University, Denmark) Giovanna Corsi (Universita' di Bologna, Italy) Giovanna D'Agostino (Universita' di Udine, Italy) Stephane Demri (LSV, ENS Cachan, France) Melvin Fitting (Lehman College, CUNY, USA) Robert Goldblatt (Victoria University of Wellington, New Zealand) Valentin Goranko (Technical University of Denmark) Rajeev Gore (Australian National University, Australia) Andreas Herzig (IRIT, Toulouse, France) Ian Hodkinson (Imperial College London, UK) Wiebe van der Hoek (University of Liverpool, UK) Alexander Kurz (University of Leicester, UK) Tadeusz Litak (University of Leicester, UK) Hiroakira Ono (Japan Advanced Institute of Science and Technology) Martin Otto (Technical University of Darmstadt, Germany) Alessandra Palmigiano (ILLC, University of Amsterdam, The Netherlands) Renate Schmidt (University of Manchester, UK) Lutz Schroeder (DFKI GmbH and University of Bremen, Germany) Valentin Shehtman (Moscow State University, Russia) Dimiter Vakarelov (Sofia University, Bulgaria) Yde Venema (ILLC, University of Amsterdam, The Netherlands) Heinrich Wansing (Ruhr University Bochum, Germany) Frank Wolter (University of Liverpool, UK) Michael Zakharyaschev (Birkbeck College, London, UK) PROGRAMME COMMITTEE CO-CHAIRS Silvio Ghilardi (Universita' degli Studi di Milano, Italy) Lawrence Moss (Indiana University, USA) ORGANIZING COMMITTEE CO-CHAIRS: Thomas Bolander (Technical University of Denmark) Torben Brauner (Roskilde University, Denmark) IMPORTANT DATES Full papers submission deadline: 16 March 2012 Full papers acceptance notification: 18 May 2012 Short presentations (abstracts) submission deadline: 1 June, 2012 Short presentations acceptance notification: 7 June, 2012 Final version of full papers and abstracts due: 15 June 2012 Conference: 22-25 August, 2012. CONFERENCE LOCATION Advances in Modal Logic 2012 will be held at the IDA conference center in downtown Copenhagen: http://ida.dk/sites/moedecenter/english/Sider/EnglishForside.aspx This is in easy walking distance from Copenhagen Central Station and a number of reasonably priced hotels. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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ordinal dependent choice
by Paul Levy 01 Jul '11

01 Jul '11

Dear all, Let alpha be an ordinal. Let $alpha be the totally ordered set of ordinals below alpha. "Alpha-dependent choice" is the following statement: for any functor A : $alpha ^ op ---> Set, if A_i is nonempty for all i < alpha, and A_i,j : A_j ---> A_i is surjective for all i <= j < alpha, then the limit of A is nonempty. If alpha has a cofinal omega-sequence (i.e. an omega-sequence of ordinals < alpha whose supremum is alpha), then alpha-dependent choice follows from dependent choice. I would think that, if alpha doesn't have a cofinal omega-sequence, then alpha-dependent choice is false. Is there a known counterexample? E.g. in the case alpha = omega_1 (the least uncountable ordinal). Thanks, Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CT2011 programme
by Steve Lack 29 Jun '11

29 Jun '11

CT2011 will take place in Vancouver, from Sunday 17 July to Saturday 23 July. The programme, up to any last-minute changes, can be found on the conference website http://www.mat.uc.pt/~ct2011/index.html I look forward to seeing you all in Vancouver. Steve Lack. (for the Programme Committee) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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size_question_bisbis
by Eduardo Dubuc 29 Jun '11

29 Jun '11

I got a private answer that made me realize I was not clear in the way I put my questions. I send now this mail with my answers, which I hope will clarify the situation. e.d. ****************** Perhaps I was not clear in my question ? It is not belived that finite sets is a small topos with finite limits and all the rest exept the axiom of infinity ? Which category of finite sets ? Of course I know they are all equivalent, but there is not a canonical small one. The answer is not, but people behave as if it were true. More comments below: > I'm replying "in private" to minimize embarrassment. > >> Consider the inclusion S_f C S of finite sets in sets. >> >> Is the category S_f closed under finite limits > > If you mean to understand, as do I, that S_f stands for the > full subcategory of the category S of sets whose objects > are the sets that happen to be finite, then: YES, of course; ... > >> ... and at the same time small ? > > ... and NO, obviously not. > >> For example, there are a proper class of singletons, all finite. Thus a >> proper class of empty limits. > > Quite so. Do you find that objectionable? > >> Question, which is the small category of finite sets ?, which are its >> objects ?. > > I don't understand either the question or its preassumptions. > Why should there be a unique ("the") category of finite sets? > Well, there is a unique category of finite sets, but it is not small, but people works as it it were. Take Joyal's theory of species. > The category S_f of finite sets discussed above isn't small. > But it has lots of equivalent, small subcategories, including > skeletal ones, the best known of which is the full subcategory > of S whose objects are the finite cardinals. Which of these > (if any) is closed under finite limits is an imponderable. Yes, what happens then when people works with a small category of finite sets and with finite limits ? >> A small site with finite limits for a topos would not be closed under >> finite limits ? > > Closed in relation to what ambient setting? The topos. > >> etc etc > > >> But, more basic is the question above: How do you define the small >> category of finite sets ? > > I *don't* define "the" small category of finite sets. > If I need *a* skeletal version of the category of finite sets, > though, I settle for that full subcategory of finite ordinals. What if I need a small category of finite sets with finite limits. Well, using choice I can produce one starting with the finite ordinals (or cardinals). Choosse a limit for each finite diagram, and keep doing this a dennumerable amount of times. >> Or only there are many small categories of finite sets ? > > So I would think :-) . Yes, me too, so this is presisely why I ask the question. > As to what follows here, I either have no answer for it, > or do not even understand the content or relevance of it: Well, I did not explain myself clearly. >> You can not define a finite limit as being any universal cone because >> then you get a large category. >> >> Then how do you determine a small category with finite limits without >> choosing (vade retro !!) some of them. And if you choose, which ones ? >> >> The esqueleton is small but a different question !! > > So if you'd like to amplify a bit, or to explain somewhat, > I'd be grateful. > > PS: I'm suddenly aware that June means WINTER in Argentina, so I hope your > questions are not merely symptomatic of a winter "brain-freeze" Well, it is not "brain freeze" yet ... or it is ? ******************************* [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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size_question_bis
by Eduardo Dubuc 29 Jun '11

29 Jun '11

The question arose by considering the usual completion into a small site with finite limits of any small set of generators. You take all finite limits of generators, and repite this dennumerable times. Then, already at the first step, you get a large subcategory. What happens ? If you choose one copy of the limit for each finite diagram, certainly it is not what it is done in the literature. If you do not choose one copy, which set of copies do you take ? Thus the completion of a set of generators into a site with finite limits depend on choice ? e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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2011 mini-WCATSS, Seattle, Aug 26-28
by Elizabeth R Henning 28 Jun '11

28 Jun '11

Below is the solicitation for the 2011 WCATSS. This is a small-scale WCATSS, and it will be more like an informal conference, by and for postdocs and grad students at all levels who are interested in algebraic topology. Please consider giving a talk--it's great for your CV, and this is a relaxed environment for inexperienced speakers. It's best to sign up by July 8, especially if you would like to be considered for funding. ---------------------------------------------------------------------- 2011 West Coast Algebraic Topology Summer School University of Washington, Seattle Dates: August 26 - 28 Hello. This year we're having a small-scale WCATSS, organized by and for grad students and postdocs. The content of the course will be based on the interests and expertise of the participants. Current topics include: Stable homotopy theory Model categories and their localization Ring spectra Triangulated categories Participants will have the opportunity to do some subset of the following: 1. give a talk about their research or a topic of interest. 2. collaborate with other grad students in planning topics and pre-lectures. 3. attend lectures outlining current research, as well as more general background pre-lectures, and extended question/answer sessions. All interested graduate students and postdocs are encouraged to visit http://2011-wcatss.wikispaces.com/ for more information. Limited travel funding is available. Or contact wcatss2011(a)gmail.com if you have questions. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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