December 2017 - Categories - categories.org.au

Book on toposes
by Olivia Caramello 24 Dec '17

24 Dec '17

Dear All, I am pleased to announce the publication of my book "Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'" (384 pages) by Oxford University Press: https://global.oup.com/academic/product/theories-sites-toposes-9780198758914 ?cc=gb&lang=en# This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes. The theory of classifying toposes - which geometrically embodies the mathematical content of first-order (geometric) theories - is first recalled, allowing the formulation of general 'bridge' principles: study theories through the computation of invariants of their associated toposes in terms of different presentations of these toposes. As any Grothendieck topos has infinitely many presentations, the expression of its invariants in terms of them gives rise to a veritable mathematical morphogenesis. These methods, which are susceptible to unify notions and results across distinct mathematical areas, are applied in particular to the study of geometric theories and their extensions through suitable topos-theoretic invariants. The book concludes with a selection of applications of the theoretical results obtained in the previous parts to very different concrete mathematical theories. All the best, Olivia [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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PSSL103 in Brno --- April 7-8 2018
by loregianf＠math.muni.cz 22 Dec '17

22 Dec '17

Dear category theorists, We are pleased to announce that the 103rd Peripatetic Seminar on Sheaves and Logic will be held on the weekend of 7/8 April 2018 in Brno, Czech Republic. On April 6 there will be an introductory "pre-PSSL" afternoon hosting talks by Moritz Groth and Simon Henry, on the theme of higher category theory. The seminar welcomes talks on topics related to any flavour of category theory and its applications, and it is in particular dedicated to PhD students and young researches. Please let us know if you would like to participate and give a talk by providing an abstract on the website of the conference (if the registration form tells you an error occurred, please email us at pssl103brno(a)gmail.com) https://www.math.muni.cz/~loregianf/PSSL103/PSSL103.php Brno is easily accessible from the UK with direct flights from London Stansted, and is also near to Vienna, Bratislava and Prague. Regular train connections depart from Prague and Vienna. Further information about travel and accommodation will appear on the conference website, and we will send a second announcement soon with further details. We hope to see you in Brno! the organizers John Bourke, Ivan Di Liberti, Simon Henry, Michael Liebermann, Fosco Loregian, Masaryk University. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CMCS 2018: Final Call for Papers
by Corina Cirstea 21 Dec '17

21 Dec '17

Call for Papers The 14th International Workshop on Coalgebraic Methods in Computer Science (CMCS'18) Thessaloniki, Greece, 14 - 15 April 2018 (co-located with ETAPS 2018) www.coalg.org/cmcs18 Flyer --------- This call for papers is available as a flyer, which can also be printed and used as a poster, at http://www.coalg.org/cmcs18/files/2017/10/cmcs18_flyer.pdf Objectives and scope -------------------- Established in 1998, the CMCS workshops aim to bring together researchers with a common interest in the theory of coalgebras, their logics, and their applications. As the workshop series strives to maintain breadth in its scope, areas of interest include neighbouring fields as well. Topics of interest include, but are not limited to, the following: - the theory of coalgebras (including set theoretic and categorical approaches); - coalgebras as computational and semantical models (for programming languages, dynamical systems, term rewriting, etc.); - coalgebras in (functional, logic, answer set, object-oriented, concurrent, and constraint) programming; - coalgebraic data types, type systems and behavioural typing; - coinductive definition and proof principles for coalgebras (including "up-to" techniques); - coalgebras and algebras; - coalgebras and (modal) logic; - coalgebraic specification and verification; - coalgebra and control theory (notably of discrete event and hybrid systems); - coalgebra in quantum computing; - coalgebra and game theory; - tools exploiting coalgebraic techniques. Venue and event --------------- CMCS'18 will be held in Thessaloniki, Greece, co-located with ETAPS 2018, on 14 - 15 April 2018. Keynote speaker --------------- Samson Abramsky (University of Oxford, United Kingdom) Invited speakers ---------------- Clemens Kupke (University of Strathclyde, United Kingdom) Daniela Petrisan (University Diderot Paris 7, France) Invited tutorial speakers ------------------------- There will be a special session on quantum computation, with invited tutorials by Bob Coecke (University of Oxford, United Kingdom) Aleks Kissinger (Radboud University Nijmegen, The Netherlands) Important dates --------------- Abstract regular papers 5 January 2018 Submission regular papers 12 January 2018 Notification regular papers 12 February 2018 Camera-ready copy 19 February 2018 Submission short contributions 23 February 2018 Notification short contributions 9 March 2018 Proceedings ----------- The proceedings of CMCS 2018 will include all accepted regular papers and will be published post-conference as a Springer volume in the IFIP-LNCS series. Accepted short contributions will be bundled in a technical report. Programme committee ------------------- Filippo Bonchi (University of Pisa, Italy) Marcello Bonsangue (LIACS, Leiden University, The Netherlands) Corina Cirstea (University of Southampton, United Kingdom) Fredrik Dahlqvist (University College London, United Kingdom) Ugo Dal Lago (University of Bologna, Italy) Sergey Goncharov (FAU Erlangen-Nürnberg, Germany) Helle Hvid Hansen (Delft University of Technology, The Netherlands) Ichiro Hasuo (National Institute of Informatics, Japan) Bart Jacobs (Radboud University Nijmegen, The Netherlands) Bartek Klin (University of Warsaw, Poland) Paul Levy (University of Birmingham, United Kingdom) Stefan Milius (FAU Erlangen-Nürnberg, Germany) Lawrence Moss (Indiana University, United States) Dirk Pattinson (Australian National University, Australia) Dusko Pavlovic (University of Hawai‘i at Mānoa, United States) Daniela Petrisan (University Diderot Paris 7, France) Damien Pous (CNRS, ENS Lyon, France) Juriaan Rot (Radboud University Nijmegen, The Netherlands) Jan Rutten (CWI/Radboud University Nijmegen, The Netherlands) Lutz Schröder (FAU Erlangen-Nürnberg, Germany) Alexandra Silva (University College London, United Kingdom) Ana Sokolova (University of Salzburg, Austria) Henning Urbat (Technische Universität Braunschweig, Germany) Jamie Vicary (University of Oxford, United Kingdom) Publicity chair --------------- Henning Basold (CNRS, ENS Lyon, France) PC chair -------- Corina Cirstea (University of Southampton, United Kingdom) Steering committee ------------------ Filippo Bonchi (University of Pisa, Italy) Marcello Bonsangue (LIACS, Leiden University, The Netherlands) Corina Cirstea (University of Southampton, United Kingdom) Ichiro Hasuo (National Institute of Informatics, Japan) Bart Jacobs (Radboud University Nijmegen, The Netherlands) Bartek Klin (University of Warsaw, Poland) Alexander Kurz (University of Leicester, United Kingdom) Marina Lenisa (University of Udine, Italy) Stefan Milius (chair), FAU Erlangen-Nürnberg, Germany Larry Moss (Indiana University, United States) Dirk Pattinson (Australian National University, Australia) Jan Rutten (CWI/Radboud University Nijmegen, The Netherlands) Lutz Schröder (FAU Erlangen-Nürnberg, Germany) Alexandra Silva (University College London, United Kingdom) Submission guidelines --------------------- We solicit two types of contributions: regular papers and short contributions. Regular papers must be original, unpublished, and not submitted for publication elsewhere. They should not exceed 20 pages in length in Springer LNCS style. Short contributions may describe work in progress, or summarise work submitted to a conference or workshop elsewhere. They should be no more than two pages. Regular papers and short contributions should be submitted electronically as a PDF file via the Easychair system at http://www.easychair.org/conferences/?conf=cmcs2018. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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SDT
by Marta Bunge 19 Dec '17

19 Dec '17

In case this interests you http://www.cambridge.org/ca/academic/subjects/mathematics/logic-categories-… Best wishes for the holidays Marta [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: How analogous are categorial and material set theories?
by Neil Barton 12 Dec '17

12 Dec '17

Thanks to everyone for their replies. I provide some quick clarifications to some of Patrik's comments below: ``You now introduce the word "core", and I would need to understand what that mathematically and logically really means, at least intuitively.'' I mean ``core'' in the trivial sense. The axioms defining what it is to be a category (of some kind) are just first-order. The same is true, of course, for ZFC. However, in the set theory context it seems at least sensible to try and provide a second-order (quasi) categoricity proof, despite the diversity of models for first-order ZFC (and indeed we have one by the work of Zermelo, Shepherdson, etc.). To attempt the same for category theory would seem to be an absurd strategy---the point of categories is that they can be instantiated in many non-isomorphic models. ``Yes, indeed, across diverse contexts, with "context" somehow related to "system" in Hidekazu Iwaki's reply involving "mathematical system".'' I cannot find Hidekazu Iwaki's reply (this is rather strange, I do not know why). However it seems like similar usage to me: I don't have a formal definition of `mathematical context', but the point is just that there's diverse non-isomorphic models where the same categorial properties pop up. e.g. (somewhat obviously for this list, but I found it striking learning some category theory) the notion of topos appears all over the place in diverse structures, and allows us to have a reasonable notion of internal logic. Your comments on the different notions of hierarchy are interesting, but I will have to think about this some more before I have anything reasonable to add. Best Wishes, Neil -- Dr. Neil Barton Postdoctoral Research Fellow Kurt Gödel Research Center for Mathematical Logic University of Vienna [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Medal for Richard Garner
by Steve Lack 12 Dec '17

12 Dec '17

Congratulations to Richard Garner, who was today awarded the Medal of the Australian Mathematical Society. Richly deserved! Steve Lack. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: How analogous are categorial and material set theories?
by Patrik Eklund 12 Dec '17

12 Dec '17

Is Category Theory a Theory? I think not. At least not in a logical sense. Is Logic a Theory. Of course not. Logic is a construction that embraces ways of creating logical theories. Can we describe Category in Logic? No, we cannot. Can we describe Logic in Category. Yes we can. Topos, and all that, even if I regret we are happy about quantifiers being adjoint functors to the contra powerfunctor. Logic should be a bit more than just that, shouldn't it? --- Can we describe Logic over Category? Yes we can. This is less recognized. This is the lative construction of logic from signatures, through terms, to sentences, and so on, as Goguen (Institutions) and Meseguer (Entailment Systems) did, without being explicit about signatures. This is Category Theory as a construction embracing ways of creating logics. We must be explicit about the starting point, the underlying signature. Just think about it, we potentially have the object of types in a monoidal category! It's just around the corner. Let's go get it, and the world will never be the same! --- Discussions under FOM now related to distinctions between first, second and third order logic is really bizarre, or boring to say the least. Much of what they try to say could be said more clearly if they would understand to use category theory as a construction site to build what they try to build. Hilbert was not a bad person, if you ask me. --- Best, Patrik [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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position
by Jiří Rosický 10 Dec '17

10 Dec '17

The Department of Mathematics and Statistics at Masaryk University invites applications for the following postdoctoral position https://www.muni.cz/o-univerzite/kariera-na-mu/volna-mista/37329 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CSL 2018 — First Call for Papers
by European Association of Computer Science Logic 10 Dec '17

10 Dec '17

First Call for Papers ======================================== Computer Science Logic 2018 Birmingham, United Kingdom 4???7 September <http://events.cs.bham.ac.uk/csl18/> ======================================== # Important Dates * Abstract Submission: 7 April 2018 (AoE) * Paper Submission: 14 April 2018 (AoE) * Notification: 14 June 2018 # The Conference Computer Science Logic (CSL) is the annual conference of the European Association for Computer Science Logic (EACSL). It is an interdisciplinary conference, spanning across both basic and application oriented research in mathematical logic and computer science. CSL 2018 will be the 27th edition in the series. It will be organised by the School of Computer Science of the University of Birmingham. # Submission Submissions will be through EasyChair. For further details please see https://easychair.org/conferences/?conf=csl18 Proceedings will be published in the Leibniz International Proceedings in Informatics. After the conference, selected papers will be invited to a special issue of the online open access journal Logical Methods in Computer Science. # Invited Speakers * To be Announced * # Programme Committee * Christel Baier, TU Dresden * Martin Berger, University of Sussex * Lars Birkedal, Aarhus University * Veronique Bruyere, University of Mons * Agata Ciabattoni, TU Wien * Ugo Dal Lago, University of Bologna * Ross Duncan, University of Strathclyde * Jamie Gabbay, Heriot-Watt University * Marco Gaboardi, University at Buffalo, SUNY * Dan R. Ghica, University of Birmingham (Co-chair) * Russ Harmer, CNRS & ENS Lyon * Achim Jung, University of Birmingham (Co-chair) * Juha Kontinen, University of Helsinki * Jean Krivine, Universit?? Paris Diderot & IRIF * Slawek Lasota, University of Warsaw * Marina Lenisa, University of Udine * Anca Muscholl, University of Bordeaux * Wied Pakusa, RWTH Aachen University * Daniela Petrisan, Universit?? Paris Diderot * Sebastian Siebertz, Univerity of Warsaw * Alexandra Silva, University College London [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Is Category Theory a Theory?
by Patrik Eklund 10 Dec '17

10 Dec '17

Thank you, Hidekazu-san, for you reply. You use several important keywords that we could debate much more, and I sincerely hope Catlist will. One word you use is "role". I find that very appealling and intriguing. What is the role of zero in the natural numbers signature? What is the role of zero as a term and number in the axiomatized number system. Does that role change and does it appear as a 'subrole' in another role? I don't know, and I am certainly overly intuitive saying so, but if we do not allow ourselves to do that, we will forever remain applying "ignorabimus", something Hilbert fiercely rejected, ending his famous radio speech with "We must know! We will know!". When I said "Is Category Theory a Theory? I think not. At least not in a logical sense." I obviously refer to "theory" as logically defined by the set of all 'clauses' we can 'infer' starting from all acceptable clauses ('axioms'), iteratively throwing them into the acceptables, and exhaustively doing that over and over again. Is Category Theory such a Theory. Of course it isn't. It's much more. If it isn't, why are we here? A monoidal category is a good example. It's not a category. It contains one, but as a structure it's not a category. Yet, monoidal categories are part of category theory. I allow myself to say that the category in a monoidal category plays a certain Role in that structure. So does the tensor, and soon we almost feel more algebraic than categorical. If we do, well, is a monoidal category then a foundation for a signature?! Signature in a broader sense, of course. Why not? We obtain expression, words, and so on. Maybe somewhere along that line somebody starts to think "What is a Turing Category?". What I try to say is that if we disallow ourselves to think in these ways, we apply that "ignorabimus". Your intuition about "role" seems to be quite rich, and I surely do not provide it with the appreciation it deserves, but I hope to hear more about it in years to come. You also use "properties", which in logic often means fixing how certain expression relate to each other. Algebra may be more fundamental than we think, and myself I am inclined to explore this more than I have before. Indeed, when in 'lativity' I underline that "signatures come first, and then we create sentences, and so on, latively", am I not actually speaking warmly about algebra being among the first ones in line? "Algebra studying itself" may be interesting to further explore, and to compare it with "logic studying itself" and "set theory studying itself". Clearly we also have "logic studying set theory", "algebra studying logic", "logic studing algebra", and in fact all combinations. Do we not even have "algebra studying how logic is studying itself", and so on? I think we do, and this really to me is one of the reasons why we sometimes so little understand each other, because we do not always clearly acknowledge what we really are doing and why, when we e.g. describe category theory as a logic, logic in a topos, categories as algebras, logic over a monoidal closed category, and so. Why do we do these things. I develop logic over monoidal closed categories because I see how underlying rich structures of a certain information scope (like health ontology) suitable can be represented because of such a category so that reasoning involving that information enables us to say more than we have used to be hearing (in health care). I am seriously starting to believe that we are able to save lives by enriching health language with category theory. So thank you once again again, Hidekazu-san, for sharing your thoughts. It is not unskillful at all, and certainly has no mistakes. It's Excellent Harmony. Looking forward to more debate on these aspects. Best regards, Patrik PS My origical catlist posting was forwarded also to FOM, in the hope that the FOM community would be even more interested to bridge foundations with aspects learned within Category Theory. That forward was rejected: "Your message was deemed inappropriate by the moderator after consulting our editors. One of them wrote: "This message seems to be mainly an expression of Eklund's personal opinions, with no supporting arguments and little clarity. I recommend rejecting it."" I replied to the fom-owner as follows: Thank you for your response. The reason why I sent it to Catlist was to raise some debate more than presenting my personal opinion. Catlist accepted it, and I thought I would bridge it over to FOM, since recently FOM has taken up an interest to undestand the role of category theory for foundations. Obviously the content was less kind and more provocative to the FOM readers, and my guess was it will be rejected. Anyway, I appreciate very much to be part of dialogue within FOM and I take this opportunity to thank you for all acceptances so far of many of my postings. My gut feeling is that foundations discussions are finding and exploring new dimensions. There are Pandora boxes around some corners, and there is resistence to open some of these. Anyway, it's all up to us, and we will all jointly continue to do the best we can. I feel very confident about what will come in 50 years from now, yet I feel sad not to live to experience it. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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