January 2017 - Categories - categories.org.au

Reference for lifting an adjunction to a monoidal one
by David Roberts 05 Feb '17

05 Feb '17

Hi all, I need a textbook or otherwise standard reference for the fact that if one has a pair of monoidal categories C, D, and an adjunction L -| R: UC <--> UD between their underlying categories, then if one of L or R lift to a (strong) monoidal functor, then the adjunction lifts to an adjunction in the 2-category of monoidal categories, strong monoidal functors and monoidal natural transformations. (Mac Lane of course only treats the case of strict monoidal functors, at least in my, older, edition of his book) Thanks, David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Conference Invitation: Higher Structures Lisbon, 24-27 July 2017
by b.gohla＠gmx.de 31 Jan '17

31 Jan '17

Dear Colleagues, Some of you may be interested in a conference we are organising. Please feel free to sign up through our website at the earliest opportunity: http://hsl2017.campus.ciencias.ulisboa.pt/ *Higher Structures Lisbon (deformation theory, operads, higher categories developments & applications)* Instituto Superior Técnico, Lisbon, 24-27 July 2017 The aim of this meeting is to stimulate interaction between people, who are working in higher structures interpreted in the broad sense (to mean higher stacks, L∞- and A∞-algebras, Batalin–Vilkovisky algebras, higher category theory, operad theory and related areas). Such flavours of higher structures have appeared in differential geometry (non-abelian and higher gerbes), rational homotopy theory, algebraic topology (string structures, extended topological quantum field theories), persistent homology, and have found a number of applications in mathematical physics, such as higher gauge theory, topological quantum field theory, possibly with defects, homological methods in quantum field theory, strings and branes, topological phases of matter, among others. On behalf of the organising committee: Aleksandar Miković (GFM/Universidade de Lisboa, Universidade Lusófona) Benjamin Alarcón Heredia (CMA/Universidade Nova de Lisboa) Björn Gohla (GFM/Universidade de Lisboa) John Huerta (CAMGSD/Universidade de Lisboa) João Faria Martins (University of Leeds) Roger Picken (CAMGSD/Universidade de Lisboa) -- Kind regards, Björn Gohla [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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YaMCATS 10 University of Leicester 13 February 2017
by Paoli, Simona (Dr.) 27 Jan '17

27 Jan '17

Dear All, The 10th meeting of the Yorkshire and Midlands Category Seminar will take place at the University of Leicester on Monday 13 February 2017. The invited speakers are Nick Gurski (University of Sheffield) Jamie Vicary (University of Oxford) Steve Vickers (University of Birmingham) Further details about the meeting can be found on the YaMCATS website. The meeting is open to all and everybody is welcome. Best wishes, The YaMCATS organizers Nicola Gambino, Nick Gurski, Simona Paoli. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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A preprint on multiple categories
by Marco Grandis 24 Jan '17

24 Jan '17

The following preprint can be downloaded: M. Grandis - R. Paré Multiple categories of generalised quintets Preprint: Pubbl. Mat. Univ. Genova, Preprint 607 (2017). Available at: http://www.dima.unige.it/~grandis/MlcGQ.pdf Abstract. We construct various multiple categories, based on generalised Ehresmann quintets. The main construction is a multiple category whose objects are all the `lax' multiple categories; the transversal arrows are their strict multiple functors while the arrows in a positive direction are multiple functors of a `mixed laxity', varying from the lax ones (in direction 1) to the colax ones (in direction \infty). ---------------- Marco Grandis (and Bob Paré) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CfP for 11th IWC 2017
by michael.heather＠trinity.cantab.net 23 Jan '17

23 Jan '17

Call for Papers for the 11th International Whitehead Conference 2017 http://whitehead2017.com/ You are invited to the 11th IWC under the topic "Nature in Process. Novel Approaches to Science and Metaphysics" 25th-28th July 2017 at the University of the Azores and to submit an abstract for presentation in any of its 16 sections by 31 JANUARY 2017 or as soon as possible. Reproduced below are the details for Section 8 on Whitehead, Mathematics and Logic where Category Theory can assist with his 'loose ends'. Current Category Theory is still founded on Whitehead's early Principia Mathematica (1912) that he soon repudiated in favour of the metaphysics of his Process & Reality (PR,1929). Today's real world problems of globalisation and higher order processes need an applicable Category Theory with a comparable shift from modelling 'up to the natural isomorphism' as in the Eilenberg-Mac Lane style of early Whitehead to the exactness of 'down from the natural isomorphism' in the metaphysics of the later Whitehead. Whitehead's search to represent our perceptions of nature as an extension of abstract space in logic was achieved only informally in his life time. Formally Alexandre Grothendieck picked up on Aristotle's metonym of the Topos for abstract space as a category but by satisfying Weil's conjectures (as appears from the Récoltes et Semailles) the Grothendieck topos was still confined to the limitations of Whitehead's early work. On the contrary the Topos in impredicative mathematics has neither the natural number object nor an initial object. For Whitehead rejects as beyond first order in abstract space the following constructs of the mind: . arithmetic (including zero and infinity) . Euclidean geometry . predication . ex absurdo reasoning . paradox (as error in antecedent reasoning) . 'vacuous actuality' (PR:xiii) Galileo's work took nearly a century to be integrated into mainstream science so we should perhaps not be too surprised with the same for Whitehead. This conference is an opportunity to contribute to these developments where they really matter -- in applicable Category Theory. ***************************************************************** 11th IWC 2017 section 8: Whitehead, Mathematics and Logic Head: Vesselin Petrov Abstract Until the end of his life Alfred North Whitehead maintained that symbolic logic was his first love. Logic dominated the mathematics of his early intellectual development at Cambridge. It was the driving force in his quest to understand process in nature and underpinned the novel approach to science and metaphysics in his subsequent influence on contemporary science and philosophy. Study of his logic and mathematics can therefore provide us with further understanding of his speculative metaphysics of nature. He would not as some sever logic from mathematics and much of his early work on mathematics was at its foundation level. Topics of interest include, but are not limited to: His initial work subsuming Grassmann's notion of logic and number into Universal Algebra and the study of axiomatics in projective and descriptive geometry with applications to the material world arising out of its own natural logic. The collaboration with Russell on the Principia Mathematica as the foundations of mainstream 20th Century mathematics, their influence on Kurt Gödel, the technical details behind why the fourth volume was abandoned and behind why they parted. Outstanding issues in Whitehead's writings particularly relating to the nature of space and time. Logical distinctions with the approaches of Kant, Poincaré, Bergson, Einstein, etc and comparison with alternative theories of extension and process. His identification of Desargues theorem as the logic behind three dimensional Euclidean space. Whitehead's theory of extension in Process and Reality as a transformation of mathematical ideas into metaphysical ones. The logic of parthood with part-whole and part-part relations as relevant today in mathematics applied to globalisation, theoretical computer science, artificial intelligence and studies in consciousness and evolutionary biology. Whitehead's informal descriptions in Process & Reality have helped spawn new subjects like mereology and contemporary mereotopology. The work of Whitehead's mature period has promoted advances on a wide front for postmodernism in the arts and humanities but these have yet to procreate postmodernism in mathematics or logic. Current topics in Whitehead's loose ends include a formal language for his cosmology of process and the clarification of his 'blind spot' for intuitionistic logic both of which are now possible to represent 'naturally' in the mathematics of Category Theory. Whitehead's last writings: Mathematics and the Good - a connection between modern mathematics and metaphysics is of importance in the philosophy of mathematics and is Whitehead's own 'footnote' on Plato's notion of Mathematics and the Good. . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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ETAPS 2017 call for participation
by Tarmo Uustalu 22 Jan '17

22 Jan '17

****************************************************************** CALL FOR PARTICIPATION ETAPS 2017 20th European Joint Conferences on Theory And Practice of Software ETAPS 2017 Uppsala, Sweden, 22-29 April 2017 http://www.etaps.org/2017 ****************************************************************** -- ABOUT ETAPS -- ETAPS is the primary European forum for academic and industrial researchers working on topics relating to software science. ETAPS, established in 1998, is a confederation of five main annual conferences, accompanied by satellite workshops. ETAPS 2017 is the twentieth event in the series. -- MAIN CONFERENCES (24-28 April) -- * ESOP: European Symposium on Programming (PC chair Hongseok Yang, University of Oxford, UK) * FASE: Fundamental Approaches to Software Engineering (PC chairs Marieke Huisman, Universiteit Twente, The Netherlands, and Julia Rubin, University of British Columbia, Canada) * FoSSaCS: Foundations of Software Science and Computation Structures (PC chairs Javier Esparza, Technische Universität München, Germany, Andrzej Murawski, University of Warwick, UK) * POST: Principles of Security and Trust (PC chairs Matteo Maffei, Universität des Saarlandes, Germany, Mark D. Ryan, University of Birmingham, UK) * TACAS: Tools and Algorithms for the Construction and Analysis of Systems (PC chairs Axel Legay, INRIA Rennes, France, and Tiziana Margaria, LERO, Ireland) TACAS '17 hosts the 6th Competition on Software Verification (SV-COMP). -- INVITED SPEAKERS -- * Unifying speakers: Michael Ernst (University of Washington, USA) Kim G. Larsen (Aalborg University, DK) * FoSSaCS invited speaker: Joel Ouaknine (University of Oxford, UK) * TACAS invited speaker: Dino Distefano (Facebook and Queen Mary University of London, UK) -- UNIFYING PUBLIC LECTURE Serge Abiteboul (DI, INRIA Paris & ENS Cachan, France) -- INVITED TUTORIALS Véronique Cortier (LORIA, CRNS, France) Kenneth McMillan (Microsoft Research Redmond, USA) -- CONTRIBUTED PAPERS -- See the accepted paper lists at the conference website. -- SATELLITE EVENTS (22-23 April, 29 April) -- 17 satellite workshops and other events will take place before or after ETAPS 2017. Check their calls for papers and consider contributing! DICE-FOPARA, GaLoP, GaM, SynCop-PV, VerifyThis (22-23 April) FESCA, SNR (22 April) HotSpot, MBT, QAPL, SannellaFest (23 April) BX, CREST, LiVe, MARS, PLACES, VPT (29 April) -- REGISTRATION -- Early registration is until Sunday, 12 March 2017 (23:59 GMT+1). http://www.etaps.org/2017/registration -- ACCOMMODATION -- The organizers have negotiated special rates from several hotels in Uppsala. To benefit from those, follow the instructions on the conference website. The offers expire on different dates. -- HOST CITY -- Uppsala city holds a rich history, having for long periods been the political, religious and academic centre of Sweden. Uppsala University is over 500 years old and ranked among the top 100 in the World and has hosted many great scientists over the years, for instance Carl von Linné, Anders Celsius and Anders Jonas Ångström. The proximity to the capital of Sweden, Stockholm, provides additional benefits as a potential site for arranging both pre- and post congress tours, as well as for excursions or tourism. -- HOST INSTITUTION -- ETAPS 2017 is hosted by the Department of Information Technology, Uppsala University. -- ORGANIZERS Parosh Abdulla (General chair), Mohamed Faouzi Atig, Andreina Francisco, Kaj Lampka, Philipp Rümmer, Konstantinos Sagonas, Björn Victor, Wang Yi, Tjark Weber, Yunyun Zhu [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Theorem or Paradox
by Patrik Eklund 19 Jan '17

19 Jan '17

Thank you, Robin. Yes, it helps. I wasn't aware of your work, so I am happy now to see it. I will read it more carefully to connect it with my thinking. What I dare say in this quick reply is that your approach to "Turing category" is closer to what I had in mind as compared to "Category of Turing". The latter is more like a category of machines and is related to work e.g. by Betti, Kasangian, Rosebrugh, Rosenthal, and probably many others. The Rosenthal approach differs a bit from the Betti-Kasangian-Rosebrugh view, as Rosenthal brings in quantaloids and such things (which is a bit of that "stuff in between", but perhaps in another sense, I guess), i.e., really focusing on transition in machines as modules (actions). However, a category of such machines as objects does not e.g. enable to bring recursion into play, as you do. Or to put it in another way, a "Category of Turing" is a category of computabilities, in some sense, whereas a Turing category is expected to be a computability category. It's a bit similar in the community of "fuzzy", where they speak about "fuzzy logic", which it actually isn't. It's "logic with fuzzy", and "fuzzy logic" is different. Understanding many-valuedness from the viewpoint of quantales and modules is a bit related to both areas, I think. It's my gut feeling. I need to read your descriptions more carefully. Partial is part of it, and I've always been scared about partial functions, but perhaps I shouldn't be. You also involve cartesian so I will try to find monoidal closedness in there. This, to me intuitively, may be somehow related a bit to Thue 1914, i.e., not just using rewrite rules on words built upon an alphabet and using a binary operation, but indeed using the tensor in a monoidal closed category. Of course, we do not have "free monoidal categories" in this required sense, so it is still open to me what happens when we try to invoke recursion into categories. You indeed have it in some form, so I will now read more carefully, and probably come back to you when I fail to understand, which I frequently do. This is a good one, so thanks again. And thanks also for the "can't have the cake and eat it". You're right on target. Best, Patrik PS Maybe such enriched models of computations are needed to understand things like global warming? Obviously, hypothesis testing won't suffice. I.e. a BIGGER question (referring to your BIG question in your 2007 slides) might be "Can we turn this way of computing into real world applications?" On 2017-01-19 03:08, Robin Cockett wrote: > Some more comment on Godel's theorem: > > > In my Estonia notes on Turing categories there is a section in which I > prove Godel's theorem for a Turing category with a "provability" > predicate. > > > http://pages.cpsc.ucalgary.ca/~robin/talks/estonia-winter-2010/estonia-note… > > > It also contains some general comments about the Godel's theorem > (which I hope you like :-)). See section 7.5. > > > The main point of the theorem from a categorical perspective is to > show that one cannot have a provability predicate (extensional) and a > setting in which there are only two subobjects of 1 (namely empty > subobject and the whole thing). This is dramatic enough as it means > mere truth and falsity does not suffice there must be stuff in between > (lots of it)! > > > The theorem in the notes is a bit more general than Joyal's theorem > but also weaker in the sense that there is an assumption of a > "provability" predicate. Well you can't have your cake and eat it! > > > Hope this helps ... > > > -robin > > (Robin Cockett) > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Theorem or Paradox
by Patrik Eklund 19 Jan '17

19 Jan '17

Since the Incompleteness Theorem uses the Liar Paradox, why is it called the Incompleteness Theorem and not the Incompleteness Paradox? A Theorem closes a development or debate, and calls for admiration (because the inventor did something supposedly good), whereas a Paradox opens up development and debate (since the detector has pointed at something being wrong), and delays the call for admiration of the disruptively innovative solution until it is really deserved. Best, Patrik -- Prof. Patrik Eklund Ume?? University Department of Computing Science SE-90187 Ume?? Sweden ------------------------- mobile +46 70 586 4414 website www8.cs.umu.se/~peklund [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Fibred 2-category of Grothendieck toposes?
by Steve Vickers 17 Jan '17

17 Jan '17

This picks up a thread from a month ago, regarding an idea that Grothendieck toposes, interpreted generally as geometric morphisms bounded over the codomain base topos, might be treated in a 2- (or bi-)fibrational way over a variable base. I have now completed a paper "Arithmetic universes and classifying toposes" that does this. It is submitted to arXiv, and meanwhile available at http://www.cs.bham.ac.uk/~sjv/papersfull.php#AUClTop The arithmetic universes enter in via a logic interpretable in any elementary topos with nno. The "arithmetic" reasoning gives topos results that are base-independent and also "geometric", in the sense that when the base varies along a geometric morphism, the classifying topos transforms by pseudopullback. Steve. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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ICLP 2017 - Call for Papers
by Son Cao Tran 14 Jan '17

14 Jan '17

Call for Papers 33rd International Conference on Logic Programming (co-located with CP and SAT and following IJCAI) Melbourne, Australia August 28 - September 1, 2017 http://iclp17.a4lp.org Conference Scope ---------------- Since the first conference held in Marseille in 1982, ICLP has been the premier international conference for presenting research in logic programming. Contributions are sought in all areas of logic programming, including but not restricted to: - Theory: Semantic Foundations, Formalisms, Nonmonotonic Reasoning, Knowledge Representation. - Implementation: Compilation, Virtual Machines, Parallelism, Constraint Handling Rules, Tabling. - Environments: Program Analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing. - Language Issues: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Programming Techniques. - Related Paradigms: Inductive and Co-inductive Logic Programming, Constraint Logic Programming, Answer-Set Programming, SAT-Checking. - Applications: Databases, Big Data, Data Integration and Federation, Software Engineering, Natural Language Processing, Web and Semantic Web, Agents, Artificial Intelligence, Bioinformatics, and Education. In addition to the presentations of accepted papers, the technical program will include invited talks, advanced tutorials, the doctoral consortium, and several workshops. Important Dates (RP: Regular Paper / TC: Technical Communication) ----------------------------------------------------------------- RP registration (abstract): 6 March, 2017 RP submission: 13 March, 2017 First notification (RPs): 24 April, 2017 TC submission (extra round): 1 May, 2017 Revision submission (RPs): 15 May, 2017 Final notifications (RPs + TCs): 29 May, 2017 Camera-ready copy (RPs + TCs): 19 June, 2017 Conference: 28 Aug / 1 Sep, 2017 Submission Details ------------------ All submissions must be made via the EasyChair conference system (http://www.easychair.org/conferences/?conf=iclp2017) Submissions of regular papers (RPs) must follow the condensed TPLP format (template available from ICLP???s web page) and not exceed 14 pages including bibliography. RPs may be supplemented with appendices for proofs and details of datasets which do not count towards the page limit and which will be available as appendices to the published paper. Three kinds of RPs will be accepted: * Technical papers for technically sound, innovative ideas that can advance the state of logic programming; * Application papers that impact interesting application domains; * System and tool papers which emphasize novelty, practicality, usability, and availability of the systems and tools described. Application, system, and tool papers need to be clearly marked in their title. All submissions must be written in English and describe original, previously unpublished research, and must not simultaneously be submitted for publication elsewhere. These restrictions do not apply to previously accepted workshop papers with a limited audience and/or without archival proceedings. Papers of the highest quality will be selected to be published in the journal of Theory and Practice of Logic Programming (TPLP), Cambridge University Press (CUP). In order to ensure the quality of the final version, papers may be subject to more than one round of refereeing (within the decision period). The program committee may recommend some RPs to be published as Technical Communications (TCs). TCs will be published by Dagstuhl Publishing in the OpenAccess Series in Informatics (OASIcs). TCs must follow the OASIcs format (template available from ICLP???s web page) and not exceed 14 pages excluding the bibliography and a short appendix (up to 5 more pages). TC???s authors can also elect to convert their submissions into extended abstracts, of 2 or 3 pages, for inclusion in the OASIcs proceedings. This should allow authors to submit a long version elsewhere. There is also a second submission round only for TCs. Submissions to this extra round must also follow the OASIcs format indicated above. RPs accepted as TCs do not need to be resubmitted to the TC extra round. Rejected RPs cannot be resubmitted as TCs. All RPs and TCs will be presented during the conference. Authors of accepted papers will, by default, be automatically included in the list of ALP members, who will receive quarterly updates from the Logic Programming Newsletter at no cost. Conference Organization ----------------------- General Chairs: Maria Garcia de la Banda Monash University, Australia Guido Tack Monash University, Australia Program Chairs: Ricardo Rocha University of Porto, Portugal Tran Cao Son New Mexico State University, USA Workshop Chair: Enrico Pontelli New Mexico State University, USA Publicity Chair: Tommaso Urli Australian National University, Australia Sponsorship Chair: Maria Garcia de la Banda Monash University, Australia Doctoral Consortium Chair (joint event with CP and SAT): Neda Saeedloei University of Minnesota Duluth, USA Christopher Mears Monash University, Australia Programming Contest Chairs: Paul Fodor Stony Brook University, USA Graeme Gange University of Melbourne, Australia Web Presence: Tommaso Urli Australian National University, Australia Program Committee ----------------- TBA Workshops --------- The ICLP 2017 program will include several workshops. They are perhaps the best places for the presentation of preliminary work, underdeveloped novel ideas, and new open problems to a wide and interested audience with opportunities for intensive discussions and project collaboration. Doctoral Consortium ------------------- The Thirteen Doctoral Consortium (DC) on Logic Programming [this year being co-organized and taking place together with CP 2017 and SAT 2017] provides research students with the opportunity to present and discuss their research directions, and to obtain feedback from both peers and experts in the field. Accepted participants will receive partial financial support to attend the event and the main conference. The best paper from the DC will be given the opportunity to present in a session of the main ICLP conference. Doctoral consortium position papers, of between 10 and 14 pages, will also be published as TCs. Conference Venue ---------------- The venue will be the Melbourne Convention and Exhibition Centre. Melbourne is the second most populous city in Australia and the coastal capital of the south-eastern Australian state of Victoria. Set on the shores of beautiful Port Phillip Bay, Melbourne has been named the World???s Most Liveable City for six years running and it is widely recognised as the cultural and culinary capital of Australia. It is a safe, creative and multi-cultural city full of exciting places to see, delicious foods to eat, and excellent events to experience; from the Arts precinct to the river bank parks and gardens to the buzzing city centre and the hidden thrills of Melbourne???s laneways. It is also an air-hop away from breathtaking destinations like The Great Barrier Reef, Sydney and Uluru. The Melbourne Convention and Exhibition Centre (MCEC) is located on the banks of the iconic Yarra River in Melbourne's South Wharf. Given its central location, it has a huge variety of accommodation close-by, with more than 6000 rooms within walking distance. MCEC is easily accessible by public transport, particularly as the Melbourne's city centre has a free tram zone that makes it easier for tourists to move around the city. Related Events -------------- Several other AI events will be held in Melbourne and other parts of Australia close to these dates, offering attendees a variety of choices for an extended itinerary. These events will include the International Conference on Principles and Practice of Constraint Programming (CP 2017) and the International Conference on Theory and Applications of Satisfiability Testing (SAT 2017), both co-located with ICLP 2017. The International Joint Conference on Artificial Intelligence (IJCAI 2017), the Australasian Joint Conference on Artificial Intelligence (AusAI 2017), the Australasian Conference on Data Mining (AusDM 2017), and the International Conference on Knowledge Science, Engineering, and Management (KSEM 2017) will all to be held in Melbourne one week before ICLP. The International Conference on Machine Learning (ICML 2017) will also be held in Sydney Australia shortly before ICLP 2017. Sponsor ------- The conference is sponsored by the Association for Logic Programming (ALP). Financial Assistance -------------------- The Association for Logic Programming has funds to assist financially disadvantaged participants and, especially, students to enable them to attend the conference. Inquiries should be made to the general chairs. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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