November 2013 - Categories - categories.org.au

Partial functor
by David Leduc 16 Mar '15

16 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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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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JLC Special Issue: Logics for Resources, Processes, and Programs
by David Pym 29 Nov '13

29 Nov '13

********************************************************************************* Call for Papers JOURNAL OF LOGIC AND COMPUTATION Special Issue on Logics for Resources, Processes, and Programs Editors: Didier Galmiche (Université de Lorraine --- LORIA) and David Pym (UCL) Submission deadline: 28 February, 2014 ********************************************************************************* AIMS AND SCOPE We invite submissions to a Special Issue of the Journal of Logic and Computation (JLC) devoted to the topic `Logics for Resources, Processes, and Programs'. This call follows on from the LRPP 2013 workshop held in association with Tableaux 2013. This Call is open to all interested authors, irrespective of attendance at LRPP 2013. Topics of interest include, but are not restricted to, the following: - Logics for resources: semantics, model theory, and proof theory; - Process calculi, concurrency, and resource-distribution; - Reasoning about programs, systems, and behaviours (e.g., Separation Logic and associated ideas); - Extensions of logics: for example, with modalities; - Languages of assertions, and languages based on resource logics (e.g., query languages, pointers, trees, and graphs); - Theorem proving and model checking in resource logics: decision procedures, strategies, complexity results; - Applications to access control models in computer and system security. We aim to identify and present a timely record of the leading contributions to these logically rich and highly applicable topics in a rigorous logic journal. SUBMISSIONS Papers should be sent by email to either of the editors (Galmiche or Pym, at their addresses as given below). Please use the Subject line: JLC LRPP submission. Papers should be prepared using LaTeX and, in the first instance, submitted as pdf. Submissions should present original work of the highest quality, not previously published in, or submitted to, another journal. Each submission will be considered by at least two reviewers and assessed against the usual high standards of the JLC. Please see http://logcom.oxfordjournals.org for guidance to authors concerning submissions to the JLC. IMPORTANT DATES Submissions: 14 March, 2014 Notifications: 15 June, 2014 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: preprint
by Marco Grandis 27 Nov '13

27 Nov '13

Dear Jean, Within directed algebraic topology (dat) and for (perhaps) all researchers working in this domain, a category is by itself a 'directed structure' while a groupoid is not (or trivially so): - a topological space has a fundamental groupoid, - a directed topological space (in each of its versions) has a fundamental category, - a directed topological space (in each of its versions) has an 'opposite object', whose fundamental category is the opposite of the previous one. I hope this clarifies our use of the term 'directed' in connection with category theory. Thank you for your interest in my book, and more generally in dat - I think it is a fascinating subject. Best regards Marco PS By the way, the French term for dat is - as far as I know - "topologie algebrique dirigee", not "directe". I think it is a good choice. M On 27 Nov 2013, at 09:40, Jean Bénabou wrote: > Dear Marco, > > Many thanks for your explanations, and of course for giving me the > possibility to study your book, which I shall do very soon. > > I have a notion which I hesitated to call directed category for > fear of a conflict in using the word directed. Your non technical > use of this word encourage me to use it, but I shall first read > your book before I make up my mind. > > Best regards, Jean > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: preprint
by Marco Grandis 27 Nov '13

27 Nov '13

Dear Jean, Presheaves on all finite ordinals are called augmented simplicial sets. As to 'directed space' I use now this term in a non-technical sense, as referring to any topological structure suitable for directed algebraic topology, like: - preordered topological space, - d-space, i.e. space with distinguished paths, - c-space, i.e. space with distinguished cubes, - etc. See my book on 'Directed Algebraic Topology'. Thanks to Cambridge Un. Press, it can be freely (and legally) downloaded from: http://www.dima.unige.it/~grandis/BkDAT_page.html (When I first used the term 'directed space', it was equivalent to d- space; later I thought it was better to keep it for a more general meaning.) Best wishes Marco [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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preprint
by Marco Grandis 25 Nov '13

25 Nov '13

The following preprint is available: ------- E. Carletti - M. Grandis Fundamental groupoids as generalised pushouts of codiscrete groupoids Dip. Mat. Univ. Genova, Preprint 603 (2013). http://www.dima.unige.it/~grandis/GpdClm.pdf Abstract. Every differentiable manifold X has a good cover, where all open sets and their finite intersections are contractible. Using a generalised van Kampen theorem for open covers we deduce that the fundamental groupoid of X is a generalised pushout of codiscrete groupoids and inclusions. This fact motivates the present brief study of generalised pushouts. In particular, we show that every groupoid is up to equivalence a generalised pushout of codiscrete subgroupoids, and that (in any category) finite generalised pushouts amount to ordinary pushouts and coequalisers. ------- Before submitting it, I would like to know if the generalised pushouts we are using (or similar colimits) have been considered elsewhere. (They are not simply connected colimits, in the sense of Bob Pare, and indeed they cannot be constructed with pushouts.) With best regards to all colleagues and friends. In particular to Ronnie Brown and Bob Pare, whose results are used in this preprint. Marco [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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8th Scottish Category Theory Seminar: final programme
by Alex Simpson 22 Nov '13

22 Nov '13

******************************************************************** *** *** 8th Scottish Category Theory Seminar *** Friday 29 November 2013, 13:30-17:30 *** International Centre for Mathematical Sciences *** 15 South College Street, Edinburgh, UK *** *** http://homepages.inf.ed.ac.uk/als/SCT/sct131129.html *** ******************************************************************** We are pleased to announce the Eighth Scottish Category Theory Seminar. Everyone is welcome. The final programme is: 1.30-2 COFFEE 2-3.00 Urs Schreiber: Higher toposes of laws of motion 3-3.30 Vincent Danos: Conditional expectation as a functor 3.30-4 COFFEE & PASTRIES 4-4.30 Ross Duncan: Quantum computing in (almost) any category: an introduction to the ZX-calculus 4.30-5.30 Bart Jacobs: Program semantics, according to Heisenberg and to Schroedinger Abstracts will be available soon at the web address above. If you wish to attend the meeting or would like to join us for dinner afterwards, you are requested to email scotcats(a)cis.strath.ac.uk Many thanks to the Glasgow Mathematical Journal Trust and to the Complex Systems Engineering and Modelling and Abstraction themes of the Scottish Informatics and Computer Science Alliance for generous financial support. Scottish Category Theory Seminar organisers: Neil Ghani, Tom Leinster, Alex Simpson (local organiser) -- Alex Simpson, LFCS, School of Informatics, Univ. of Edinburgh, UK Email: Alex.Simpson(a)ed.ac.uk Tel: +44 (0)131 650 5113 Web: http://homepages.inf.ed.ac.uk/als Fax: +44 (0)131 651 1426 -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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subgroupoids of V-categories
by Emily Riehl 20 Nov '13

20 Nov '13

Hi all, For general V (closed symmetric monoidal, bicomplete), is there a general way to construct the maximal subgroupoid of a V-category C? I think I know how to *detect* the maximal subgroupoid. A map in C is an isomorphism iff it is representably so: Writing 1 for the monoidal unit, we say f : 1 -> C(x,y) is an iso iff the induced map f_* : C(z,x) -> C(z,y) is an iso in V for all z. So we might say that a V-category G with the same objects and C and an identity-on-objects local monomorphism G -> C is the maximal subgroupoid provided that a morphism f factors through G(x,y) -> C(x,y) just when f is an isomorphism. In examples, this is probably good enough, but I still would feel better if I had a general construction of the maximal subgroupoid. I feel like this should be some sort of weighted limit, perhaps with some additional structure on V? Thanks, Emily [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Questions on compact closed categories
by Peterson Clayton 19 Nov '13

19 Nov '13

Dear list members, I am currently working in categorical logic with something that might be called a "compact closed deductive system", that is, a deductive system (in the sense of Lambek) defined as a compact closed category (i.e., a *-autonomous category where the tensor unit is a dualizing object). I have two questions. First, it appeared to me that we can show in a compact closed deductive system that every arrow is an isomorphism. Hence, if there is a deduction arrow from A to B, then A is isomorphic (logically equivalent) to B. Is this result accurate? Does this generalize to any compact closed category? Secondly, I wonder what happens if we add an arbitrary arrow A --> B to the category. Put differently, what happens if we add A --> B as an axiom to a compact closed deductive system? Does this also yield an isomorphism between A and B (assuming that the first result is adequate)? Or is it possible to add some axioms that are not necessarily isomorphisms? I hope my question is clear, and if not I would be happy to clarify myself, so do not hesitate to contact me. Any lead will be appreciated. Thanks in advance for those who will respond. Yours, Clayton Peterson Ph. D. candidate Université de Montréal clayton.peterson(a)umontreal.ca [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Special Session on Categorical Topology (AMS-MAA JMM, 2014)
by Gavin Seal 19 Nov '13

19 Nov '13

Dear Colleagues, There will be a Special Session on Categorical Topology at the AMS-MAA Joint Mathematics Meetings in Baltimore, MD, on Saturday January 18, 2014, from 8:00 to 18:00. The following people will be giving talks: Michael Barr (McGill University) Hatim Boustique (Valencia College) Jean Goubault-Larrecq (ENS Cachan) Gábor Lukács (Halifax) Frédéric Mynard (Georgia Southern University) Gary Richardson (University of Central Florida) Gavin Seal (EPFL) Andrzej A Szymanski (University of Pennsylvania) Walter Tholen (York University) The schedule and further information can be found at: http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_…. We still have one or two 20-minute slots available if you are interested in giving a talk. In such a case, please contact me <gavin.seal(a)fastmail.fm> or Frederic Mynard <fmynard(a)georgiasouthern.edu>. Note however that because of the conference deadlines, these talks will not appear in the official program. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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