May 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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Willams Lecture
by Peter Freyd 01 Jun '11

01 Jun '11

If one goes to itunes or ipod and searches for "antiphilosophy" you will find two free downloads (one with and one without video) for "An Anti-philosophy of Mathematics." I attempt therein to give a definition of math. (Before you get there you might first be taken to a page that gives you a choice of "Lectures and Events..." or "The music of Awannabepoet." Choose the first: it leads to a chronological list of the Williams Lectures at Penn and antiphilosophy appears at the end.) You might well skip the first 14 minutes and 50 seconds (it's mostly about the 1960s history of the Penn philosophy department. Just in case you do watch it, the Aravind I refer to after the first 6 minutes is Aravind Joshi sitting in the audience, the distinguished computer scientist best known for his "tree-adjoining grammars" in linguistics). If you get as far as 42:40 I start answering questions and, as usual, on these things, you can't hear them being asked. So here's something of a list: 42:40 Zoltan Domotor asks if my definition sheds light on issues of objectivity and truth in mathematics. 50:20 Someone asks if my definition depends on assumptions about the world 53:00 I forgot this question most likely because -- as becomes evident -- I didn't answer it. 55:15 Murray Gerstenhaber asks if math [just as every other subject, I might add] is defined by the questions that are asked and don't those questions ask themselves anyway. 1:02;15 "How can we be non-arbitrary in this arbitrary world?" 1:04:00 A question about machine proofs. 1:06:20 "Would your analysis lead to a 'fusion' of logicism and formalism?" Which --,wonderfully enough -- immediately took me into the coda I had planned. If you listen and don't see the video, it's worth knowing that I only twice used a projected image. The first use -- it appears at the very beginning -- displays the following email I had received (from an author who insists on not being identified}: How could you? An "Antiphilosophy" for mathematics? You -- who sat at the feet of Curt Ducasse, Wesley Salmon, Stephan Korner, Roderick Chisholm, Carl Hempel, Alonzo Church, Kurt Godel, John Myhill, Ernest Nagel, Marvin Farber, Nelson Goodman, Dana Scott, Stanley Tennenbaum, Paul Bernays, Alfred Tarski -- you're now an antiphilosopher? Please: tell me it's a hoax. The other projected image (at 21:50) was a web page that can be found at: http://www.math.harvard.edu/history/peirce_algebra/005.html It shows the famous opening line of Benjamin Peirce's "Linear Associative Algebra," to wit: Mathematics is the science which draws necessary conclusions. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Professorship in Adelaide
by Ross Street 01 Jun '11

01 Jun '11

A new professor job at Adelaide has just been advertised:- http://www.adelaide.edu.au/jobs/current/7265/ Also useful are tips on applying for jobs at Adelaide:- http://www.adelaide.edu.au/staff/future/apply/ The selection criteria are very important to address carefully and thoroughl= y, which is unlike jobs in the northern hemisphere.=20 Ross www.math.mq.edu.au/~street [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CT2011
by Steve Lack 31 May '11

31 May '11

Dear Colleagues, This is a final reminder that the (extended) deadline for submission of abstracts is June 1. In my part of the world that is tomorrow - but I'll go by the sender's time, not mine. For instructions on preparing the abstract, including a latex template, see http://www.mat.uc.pt/~ct2011/program.html#Abstract I look forward to seeing you all in Vancouver. Regards, Steve Lack. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CALCO 2011: First Call for Participation
by Corina Cirstea 31 May '11

31 May '11

========================================================================= CALL FOR PARTICIPATION: CALCO 2011 4th International Conference on Algebra and Coalgebra in Computer Science August 29 - September 2, 2011 Winchester, UK http://calco2011.ecs.soton.ac.uk/ ========================================================================= !! REGISTRATION NOW OPEN !! Early registration deadline: July 15, 2011 ========================================================================= CALCO aims to bring together researchers and practitioners with interests in foundational aspects, and both traditional and emerging uses of algebras and coalgebras in computer science. This is a high-level, bi-annual conference formed by joining the forces and reputations of CMCS (the International Workshop on Coalgebraic Methods in Computer Science), and WADT (the Workshop on Algebraic Development Techniques). Previous CALCO editions took place in Swansea (Wales, 2005), Bergen (Norway, 2007) and Udine (Italy, 2009). The fourth edition will be held in the city of Winchester (UK), a historic cathedral city and the ancient capital of Wessex and the Kingdom of England. CALCO 2011 will be preceded by the CALCO Young Researchers Workshop, CALCO-Jnr, dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. The programme of CALCO will also comprise presentations of tools based on algebraic and/or coalgebraic principles, that have been selected in the context of a dedicated workshop, CALCO-Tools. -- INVITED SPEAKERS -- * Vincent Danos (UK): Energy as Syntax * Javier Esparza (Germany): Solving Fixed-Point Equations by Derivation Tree Analysis * Philippa Gardner (UK): Abstract Local Reasoning about Program Modules * Gopal Gupta (USA): Infinite Computation, Coinduction and Computational Logic -- CALCO ACCEPTED PAPERS -- * Clement Fumex, Neil Ghani and Patricia Johann. Indexed Induction and Coinduction, Fibrationally * Jort Bergfeld and Yde Venema. Model constructions for Moss' coalgebraic logic * Jiri Adamek, Mahdie Haddadi and Stefan Milius. From Corecursive Algebras to Corecursive Monads * Sergey Goncharov and Lutz Schroeder. A Counterexample to Tensorability of Effects * Camilo Rocha and Jose Meseguer. Proving Safety Properties of Rewrite Theories * Ekaterina Komendantskaya and John Power. Coalgebraic semantics for derivations in logic programming * Adriana Balan and Alexander Kurz. Finitary Functors: from Set to Preord and Poset * Joost Winter, Marcello Bonsangue and Jan Rutten. Context-Free Languages, Coalgebraically * Marta Bilkova, Alexander Kurz, Daniela Petrisan and Jiri Velebil. Relation Liftings on Preorders * Murdoch Gabbay, Tadeusz Litak and Daniela Petrisan. Stone duality for nominal Boolean algebras with `new': topologising Banonas * Bart Jacobs. Bases as Coalgebras * Thorsten Altenkirch, Peter Morris, Fredrik Nordvall Forsberg and Anton Setzer. A categorical semantics for inductive-inductive definitions * Jun Kohjina, Toshimitsu Ushio and Yoshiki Kinoshita. Coalgebraic Approach to Supervisory Control of Partially Observed Mealy Automata * Ichiro Hasuo. The Microcosm Principle and Compositionality of GSOS-Based Component Calculi * Mihai Codescu and Till Mossakowski. Refinement trees: calculi, tools and applications * Baltasar Trancon Y Widemann and Hauhs Michael. Distributive-Law Semantics for Cellular Automata and Agent-Based Models * Corina Cirstea. Model Checking Linear Coalgebraic Temporal Logics: an Automata-Theoretic Approach * Katsuhiko Sano. Generalized Product of Coalgebraic Hybrid Logics * Rasmus Ejlers Mogelberg and Sam Staton. Linearly-used state in models of call-by-value * Fredrik Dahlqvist and Dirk Pattinson. On the fusion of coalgebraic modal logics * Manuel A. Martins, Alexandre Madeira, Razvan Diaconescu and Luis Barbosa. Hybridization of Institutions -- CALCO-Tools ACCEPTED PAPERS -- * Luca Aceto, Georgiana Caltais, Eugen-Ioan Goriac and Anna Ingolfsdottir. PREG Axiomatizer - A Ground Bisimilarity Checker for GSOS with Predicates * Pawel Sobocinski and Jennifer Lantair. WiCcA: LTS generation tool for wire calculus * Francisco Duran, Camilo Rocha and Jose Maria Alvarez. Tool Interoperability in the Maude Formal Environment * Andre Martins, Luis Barbosa and Nuno Rodrigues. SHACC: A functional animator for a component calculus * Ulrich Berger, Kenji Miyamoto, Helmut Schwichtenberg and Monika Seisenberger. Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras * Musab Alturki and Jose Meseguer. PVeStA: A Parallel Statistical Model Checking and Quantitative Analysis Tool -- LOCATION -- Winchester is a beautiful historic city in southern England, known for its 11th-century cathedral and 12th-century castle. It is located just under an hour by rail from London Waterloo, and 15 minutes by road or rail from Southampton Airport. London Heathrow is 50 miles away and London Gatwick 72 miles away. -- GRANTS -- CALCO has limited funds to support the attendance of PhD students. Details on how to apply are available on the CALCO 2011 website. -- FURTHER INFORMATION -- Queries should be emailed to calco2011(a)ecs.soton.ac.uk . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Gray tensor product
by Ross Street 30 May '11

30 May '11

Dear Mike Perhaps my notes on the subject at http://www.math.mq.edu.au/~street/GrayTensor.pdf will help a bit. Ross www.math.mq.edu.au/~street Sent from my iPad On 27/05/2011, at 1:57 AM, Mike Stay <metaweta(a)gmail.com> wrote: > Has anyone "unpacked" the meaning of the Gray tensor product of strict > 2-categories? I'm looking for something like "the Gray product C > tensor D is the 2-category whose > - objects are pairs (c,d) > - morphisms are ... > - 2-morphisms are ..." > > My higher-category-fu isn't strong enough yet to grok the implicit definition > 2Cat(C tensor D, E) ~= 2Cat(C, Ps(D,E)), > where Ps(D,E) is the 2-category of 2-functors D->E, pseudonatural > transformations, and modifications. > -- > 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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Re: Gray tensor product
by Steve Lack 28 May '11

28 May '11

Dear Mike, the objects, as you say, are pairs (c,d) consisting of an object of C and an object of D morphisms are freely generated by those of the form (f:c->c',1_d:d->d) and (1_c:c->c,g:d->d') subject to the relations (f',1)(f,1)=(f'f,1) and (1,g')(1,g)=(1,g'g). (this is very similar to the description of the elements of the tensor product of two abelian groups). 2-cells are best described by the fact that there is a 2-functor from the Gray tensor C@D to the product CxD which is the identity on objects and on the generating 1-cells, and is locally fully faithful (fully faithful on 2-cells). Thus this 2-functor C@D->CxD is in fact a biequivalence. On 27/05/2011, at 9:57 AM, Mike Stay wrote: > Has anyone "unpacked" the meaning of the Gray tensor product of strict > 2-categories? I'm looking for something like "the Gray product C > tensor D is the 2-category whose > - objects are pairs (c,d) > - morphisms are ... > - 2-morphisms are ..." > > My higher-category-fu isn't strong enough yet to grok the implicit definition > 2Cat(C tensor D, E) ~= 2Cat(C, Ps(D,E)), > where Ps(D,E) is the 2-category of 2-functors D->E, pseudonatural > transformations, and modifications. > -- > 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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Re: Gray tensor product
by Mike Stay 28 May '11

28 May '11

On Fri, May 27, 2011 at 10:16 AM, Finn Lawler <flawler(a)cs.tcd.ie> wrote: > Mike Stay wrote: >> Has anyone "unpacked" the meaning of the Gray tensor product of strict >> 2-categories? I'm looking for something like "the Gray product C >> tensor D is the 2-category whose >> - objects are pairs (c,d) >> - morphisms are ... >> - 2-morphisms are ..." > > Gray's book Formal Category Theory: Adjointness for 2-Categories (Springer LNM 391) is the original reference. Theorem 4.9 constructs the 'lax' tensor product. A good reference for the 'pseudo' tensor product is chapter 5 of Nick Gurski's 2007 Ph.D. thesis 'An algebraic theory of tricategories'. Thanks to everyone! Gurski's exposition is exactly what I was looking for. -- 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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