December 2019 - Categories - categories.org.au

Re: "First" use of 'Category theory' to describe our field
by David Roberts 24 Feb '24

24 Feb '24

Dear Ross, no, that's pretty good! It's mildly surprising that it took ~20 years for the name to 'stick', but maybe less so given that the field grew slowly to start. Thanks, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com On Thu, 11 Jul 2019 at 08:21, Ross Street <ross.street(a)mq.edu.au> wrote: > > Dear David > > From memory, the Pure Mathematics Honours (USyd) course that Max Kelly taught in 1965 > was called ``Category Theory''. It concentrated on different kinds of morphisms > and factorizations in a category, and finished with adjoint functors. > Also John Gray's (UIllinois) 1968-69 graduate course had that name. > > From Eilenberg I heard that each person using categories should have their own category of expertise. > I told this to John Gray who said that was fine; the time had come for that category to be Cat. > > I would suggest that the first category theorists to think of themselves as such were Eilenberg's students at Columbia. > However, Mac Lane was definitely a category theorist. > > This is probably not the verifiable stuff you were seeking. > > Ross > > > On 10 Jul 2019, at 10:01 PM, David Roberts <droberts.65537(a)gmail.com> wrote: > > Hi all, > > the (idle) question is: when did the phrase 'category theory' catch on > for the field? Clearly it didn't leap from either of the heads of > Eilenberg or Mac Lane full-grown, since they used the phrase 'General > theory of natural equivalences'. There are the old 'Reports of the > Midwest Category Seminar' lecture notes (the first in 1967), which > hints that 'category theory' wasn't quite the name in use. > > Even more interesting: who was the first "category theorist", by that name? > > Answers referring to verifiable sources would be best. > > Thoughts? > > David > > > > David Roberts > Webpage: https://ncatlab.org/nlab/show/David+Roberts > Blog: https://thehighergeometer.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Monoidal product functor is strong monoidal, when?
by David Roberts 12 Jan '20

12 Jan '20

Hi all, I have half convinced myself (without checking details) that if I have a braided monoidal category (C,@), then the monoidal product @: C x C --> C is strong monoidal. Is this true? What's a reference for this I could point to? Thanks, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Compositionality
by John Baez 29 Dec '19

29 Dec '19

We are happy to announce the publication of the first volume of Compositionality. You can find the papers in our first volume here: https://compositionality-journal.org Compositionality is a journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline. Topics may concern foundational structures, an organizing principle, or a powerful tool. Example areas include but are not limited to: computation, logic, physics, chemistry, engineering, linguistics, and cognition. Compositionality is a diamond open access journal: free to publish in, and free to read. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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TYPES 2020 - Call for contributions, gentle remind
by Ugo de Liguoro 27 Dec '19

27 Dec '19

Call for contributions: 26th International Conference on Types for Proofs and Programs, TYPES 2020 2 - 5 March 2020, Turin https://types2020.di.unito.it/ Torino, Italy BACKGROUND The TYPES meetings are a forum to present new and on-going work in all aspects of type theory and its applications, especially in formalised and computer assisted reasoning and computer programming. The TYPES areas of interest include, but are not limited to: * foundations of type theory and constructive mathematics; * applications of type theory; * dependently typed programming; * industrial uses of type theory technology; * meta-theoretic studies of type systems; * proof assistants and proof technology; * automation in computer-assisted reasoning; * links between type theory and functional programming; * formalizing mathematics using type theory. We encourage talks proposing new ways of applying type theory. In the spirit of workshops, talks may be based on newly published papers, work submitted for publication, but also work in progress. The EUTypes Cost Action CA15123 (eutypes.cs.ru.nl) focuses on the same research topics as TYPES and partially sponsors the TYPES Conference: Part of the program is organised under the auspices of EUTypes. INVITED SPEAKERS * Ulrik Buchhotlz * Pierre Marie-P??drot * Leonardo de Moura * Sara Negri CONTRIBUTED TALKS We solicit contributed talks: Selection of those will be based on extended abstracts/short papers of 2 pp (not including bibliography) formatted with easychair.cls. The submission site is https://easychair.org/conferences/?conf=types2020. Important dates: * abstract submission: 10 January 2020, anywhere on Earth * notification of acceptance/rejection: 1 February 2020 * camera-ready version of abstract: 15 February 2019 Camera-ready versions of the accepted contributions will be published in an informal book of abstracts for distribution at the workshop. POST-PROCEEDINGS Similarly to TYPES 2011 and TYPES 2013-2019, a post-proceedings volume will be published in the Leibniz International Proceedings in Informatics (LIPIcs) series. Submission to that volume will be open to everyone. CONTACT Email: ugo.deliguoro(a)unito.it Program committee ?????? Ugo de??? Liguoro (Universit?? di Torino) (chair) ?????? Stefano Berardi (Universit?? di Torino) (co-chair) ?????? Marino Miculan (Universit?? di Udine) ?????? Marc Bezem (University of Bergen) ?????? Gilles Dowek (INRIA ??? ENS Paris-Saclay) ?????? Takeshi Tsukada (University of Tokyo) ?????? Jos?? Esp??rito Santo (University of Minho) ?????? Herman Geuvers (Radboud University Nijmegen) ?????? Ralph Matthes (IRIT ??? CNRS and University of Toulouse) ?????? Henning Basold (Universiteit Leiden) ?????? Aleksy Schubert (University of Warsaw) ?????? Anton Setzer (University of Swansea) ?????? Thorsten Altenkirch (University of Nottingham) ?????? Silvia Ghilezan (Univerity of Novi Sad) ?????? ??tienne Miquey (INRIA, University of Nantes) ?????? Elaine Pimentel (Federal University of Rio Grande do Norte) ?????? Tarmo Uustalu (Reykjavik University) ?????? Alexandre Miquel (University of the Republic, Montevideo) ?????? Thierry Coquand (Chalmers University of Technology) Organisers: Ugo de'Liguoro (University of Turin, chair) Stefano Berardi (University of Turin, co-chair) -- Ugo de'Liguoro Associate Professor of Computer Science Dipartimento di Informatica Universit?? di Torino Corso Svizzera 185, 10149, Torino, Italy [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Applied Category Theory 2020 - Adjoint School
by Paolo Perrone 25 Dec '19

25 Dec '19

Hello everyone. As in the past two years, we are organizing an Applied Category Theory conference and an adjoint school. This year the conference will take place on July 6-10, 2020. The research part of the school will be held during the week June 29-July 3, 2020. Both activities will take place at MIT <http://web.mit.edu/>. The applications for the school are now open, the deadline is January 15, 2020. The mentors and projects are going to be: - Michael Johnson, *Categories of Maintainable Relations <https://www.appliedcategorytheory.org/adjoint-school-act-2020/categories-of…>* - Nina Otter, *Diagrammatic and algebraic approaches between persistence modules <https://www.appliedcategorytheory.org/adjoint-school-act-2020/diagrammatic-…>* - Valeria de Paiva,* Dialectica categories of Petri nets <https://www.appliedcategorytheory.org/adjoint-school-act-2020/dialectica-ca…>* - Michael Shulman, *A practical type theory for symmetric monoidal categories <https://www.appliedcategorytheory.org/adjoint-school-act-2020/a-practical-t…>* More information can be found at www.appliedcategorytheory.org. The school is open to anyone, from anywhere in the world, who is interested in applying category-theoretic methods to problems outside of pure mathematics. This is emphatically not restricted to math students, but one should be comfortable working with mathematics. Knowledge of basic category-theoretic language—the definition of monoidal category for example—is encouraged. We will consider advanced undergraduates, PhD students, post-docs, as well as people working outside of academia. Members of minorities, and of any groups which are underrepresented in the mathematics and computer science communities, are especially encouraged to apply. For how to apply, see the link https://www.appliedcategorytheory.org/adjoint-school-act-2020/act-school-20… . <https://www.appliedcategorytheory.org/adjoint-school-act-2020/act-school-20…> For any questions or doubts please write us at the address* act adjoint school at gmail dot com*. Sincerely, The organizers - Carmen Constantin, Eliana Lorch, and Paolo Perrone. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Workshop "Categorical Probability and Statistics", 5-8 June 2020, Ottawa
by Tobias Fritz 23 Dec '19

23 Dec '19

Dear Categorists, this is the first announcement of the workshop "Categorical Probability and Statistics", taking place 5-8 June 2020 as part of the Canadian Mathematical Society's 75th Anniversary Summer Meeting at the University of Ottawa, and organized by myself and Rory Lucyshyn-Wright. See http://perimeterinstitute.ca/personal/tfritz/2019/cps_workshop/ for some more information. While categorical approaches to probability have been investigated both by category theorists and by statisticians since the 1960s, the past few years have seen tremendous progress, much of it driven by computer scientists, which makes a categorical foundation for probability and statistics seem feasible. The goal of this workshop is to bring together these communities for an exchange of ideas, methods and goals. Optimally, it will facilitate the emergence of a new interdisciplinary research community focusing on categorical probability and statistics. We have the following (tentative and yet incomplete) list of speakers: * Franck van Breugel * Vincent Danos * Hông Vân Lê * Bart Jacobs * Peter McCullagh * Paolo Perrone * Eigil Fjeldgren Rischel * Alexandra Silva * Robert W. Spekkens * David Spivak * Sam Staton We also hope to arrange for plenty of informal discussions outside of the talks. It would be great to see many of you there. It may help to know that another part of the Summer Meeting is Dorette Pronk's "Logic and Category Theory", and also the 28th Foundational Methods in Computer Science Workshop (http://aix1.uottawa.ca/~rblute/FMCS2020/) will take place in Ottawa directly afterwards. best regards, Tobias [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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28th Foundational Methods in Computer Science Workshop
by Richard Blute 18 Dec '19

18 Dec '19

28th Foundational Methods in Computer Science Workshop June 9-12, 2020, University Of Ottawa Foundational Methods in Computer Science is an annual workshop that brings together researchers in theoretical computer science and category theory. Past workshops have enjoyed talks in areas such as categorical quantum mechanics, restriction categories, database design, and the differential and resource logics. We will host tutorials and talks in several of these and related areas. We anticipate having talks and tutorials for the entire day on June 9,10 and 11, with the possibility of additional talks on the morning of the 12th, depending on how many talks are volunteered. The conference website is at http://aix1.uottawa.ca/~rblute/FMCS2020. This year, FMCS will immediately follow the 2020 Canadian Mathematical Society Summer Meeting, also held in Ottawa. We suggest attendees check out the schedule for that conference as there are a number of sessions of interest to category theorists. Support for graduate students: We particularly encourage graduate students to attend FMCS and to present their work. Some limited funding is available to support graduate students who wish to attend FMCS. To obtain the discounted registration and to apply for this funding you should contact one of the local organizers. Talks: Anyone interested in giving a talk or tutorial should contact the local organizers, no later than May 15th. But earlier is better. Housing: We were unable to reserve housing in the campus dorms, but there will likely be some individual rooms available. We will be listing hotels on the conference website shortly. It is recommended not to wait until the last minute to book accommodations. Registration: There will be a small registration fee. It will help to cover refreshments and subsidize students. Local Organizers: Rick Blute (rblute at uottawa dot ca) Pieter Hofstra (phofstra at uottawa dot ca) Phil Scott (philip dot scott at uottawa dot ca) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Announcement: Talbot Workshop 2020
by Opie, Morgan 14 Dec '19

14 Dec '19

The application for this year's Talbot workshop is now live. See below for details: 2020 TALBOT WORKSHOP: AMBIDEXTERITY IN CHROMATIC HOMOTOPY THEORY Mentored by Jacob Lurie and Tomer Schlank June 21 - 27, 2020 Nacogdoches, TX (to be confirmed) The Talbot Workshop is a one week learning workshop for roughly 35 graduate students and a few postdocs. Most of the talks will be given by participants, and will be expository in nature. Topic description: A primary aim of chromatic homotopy theory is to understand the stable homotopy category by decomposing it into pieces (called chromatic localizations) which are, at least in principle, easier to understand. These chromatic localizations enjoy a certain duality property called ambidexterity, which guarantees that certain homotopy limits can be understood as homotopy colimits (and vice versa). The goal of this workshop is to explain the mathematics of ambidexterity and some of its applications. More details about the program, including a preliminary list of talks and references, can be found here: http://math.mit.edu/conferences/talbot/index.php?year=2020 Applications close on Saturday, February 1 at 11:59PM Eastern time. You can apply online here: http://math.mit.edu/conferences/talbot/index.php?pageID=application Talbot is meant to encourage collaboration among young researchers, with an emphasis on graduate students. We also aim to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field -- in particular, students at all levels of graduate education are encouraged to apply. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply. We will cover all local expenses including lodging and food. We also offer partial funding for participants' travel costs. If you have any questions, please do not hesitate to e-mail the organizers at talbotworkshop (at) gmail.com. Organizers: Calista Bernard Yajit Jain Morgan Opie Lucy Yang [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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well powered categories, categorically?
by Paul Taylor 06 Dec '19

06 Dec '19

Is there some genuinely categorical account of the notion of WELL POWERED CATEGORY that would rid this topic of what I have taken to calling "hocus pocus" foundations? That is, I do not want to be told that a well powered category has a "set" of isomorphism classes of subobjects of each object. (I have just done a web search for this phrase but, despite the occurrence of several names for which I have a lot of respect, I could not find anything along the lines I have in mind.) Suppose we are using some elementary topos E as our usual mathematical workbench, so objects of E are called "sets". We can set up the notions of poset, dcpo, lattice, complete lattice and whatever in E in the usual way. To talk about some category C being "well powered", I want: - I don't care about "collecting" all the objects of C, so it doesn't need to be an internal category in E. - I would like the homs of C to be objects of E, so it is an E-enriched category. - Each object of C has a "set" (E-object) of isomorphism classes of monos into it, and - C might as well have pullbacks of monos (inverse images), so this is a contravariant functor Sub : C^op ------> Poset_E - Now I want to so some ordinary categorical constructions in C using diagrams, with such things as pullbacks, colimits of diagrams indexed by E-objects, maybe function types. - Suppose that all of the objects that occur in my construction have monos into a handful of particular C-objects X_1, ..., X_k - Then I want to INTERNALISE the construction using endofunctions of Sub (X_1 x ... x X_k) or something like that. - I use some logic and constructions in the elementary topos E to do something or other with this internalisation. - Then I want to EXTERNALISE this to give some diagrammatic construction in the category. - A particular application of this would be to PARTIAL MAPS, so maybe some of the work of Pino Rosolini, Robin Cockett and others might form part of this theory. For example, let C just be the topos E. We know how to internalise ("classify") subobjects - using the subobject classifier Omega. Simple constructions like intersection and union of subobjects in E can be internalised as the meet and join on Omega. So we can show that it is a Heyting algebra. Doing this is an exercise that many of us will have done as graduate students. It's straightforward, once you get the idea, but a bit tedious after a while. So what I'm looking for is the universal property that says how to internalise and externalise, ie translate between categorical diagram constructions in the category C and endofunctions of the Sub(X) objects in E. I will write about the subject for which I need this in another posting. Any ideas? Paul Taylor. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Several Funded Doctoral Positions in Computer Science in Austria (Vienna, Graz or Linz) - Deadline: January 11, 2020
by Mihaela Rozman 05 Dec '19

05 Dec '19

TU Wien, TU Graz, and JKU Linz are seeking highly qualified candidates for our joint doctoral program Logical Methods in Computer Science (logiCS). The LogiCS doctoral college focuses on interdisciplinary research topics covering - computational logic, and applications of logic to - databases and artificial intelligence, - computer-aided verification, - security and privacy, - cyber-physical systems, as well as to - distributed systems. THE PROGRAM Our PhD program LogiCS is focusing on logic and its applications in computer science. Successful applicants will work with and be mentored by leading researchers in the fields of computational logic, databases and knowledge representation, computer-aided verification, security and privacy, cyber-physical systems, and distributed systems. FACULTY MEMBERS M. Bartocci / A. Biere / R. Bloem / A. Ciabattoni / T. Eiter / G. Gottlob / R. Grosu / L. Kovacs / M.Maffei / M. Ortiz / U. Schmid / M.Seidl / S. Szeider / G. Weissenbacher / S.Woltran The LogiCS faculty comprises 15 renowned researchers with strong records in research, teaching and advising, complemented by 15 associated members who further strengthen the research and teaching activities of the college. POSITIONS AND FUNDING *We are looking for 8 very strong doctoral students. *We offer internationally competitive salaries funded for at least 3 years according to the funding scheme of the Austrian Science Fund (with full health benefits) *The funding can be extended for one additional year contingent on a placement at one of our international partner institutions. CURRENT RESEARCH AREAS Students can pursue doctoral research within the following areas: * Automated Software Verification * Epistemic logic in distributed computing * Game-based Semantics * Fixed-Parameter Algorithms and Complexity * Formal Verification of hybrid systems * Model Checking * Modeling and analysis of digital integrated circuits * Security and Privacy * Scheduling and logic programming * Topology in distributed computing HOW TO APPLY For more information about the PhD program and application process, as well as faculty profiles, please visit our website at: https://logic-cs.at/phd/admission/ *The applicants are expected to have completed an excellent diploma or master's degree in computer science, mathematics, or a related field. *Candidates with comparable achievements will be considered on a case-by-case basis. *Applications by the candidates need to be submitted electronically. Next application deadline: January 11, 2020. LOGIC IN AUSTRIA Austria has a highly active and successful logic in the computer science community. Recent activities include: www.arise.or.at (Austrian Research Network in Rigorous Systems Engineering) www.vcla.at (Vienna Center for Logic and Algorithms) www.kgs.logic.at (International Kurt Goedel Society) HIGHEST QUALITY OF LIFE The Austrian cities Vienna, Graz, and Linz, located close to the Alps and surrounded by beautiful nature, provide an exceptionally high quality of life, with a vibrant cultural scene, numerous cultural events, world-famous historical sites, a large international community, a varied cuisine and famous coffee houses. If you have any questions, feel free to get in touch: info(a)logic-cs.at [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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