January 2024 - Categories - categories.org.au

Lecture notes by Bill Lawvere
by Michael Barr, Prof. 22 Apr '26

22 Apr '26

I got a request from someone named C. Muster who is searching for a set of lecture notes by Bill that he gave at U. Laval in 1974. Does anyone have a copy that they would be willing to send to him. Michael You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

5 4

PhD opportunities at the University of Birmingham
by Paul Levy 24 Nov '24

24 Nov '24

* Imminent funding deadline (1 December) - please contact us immediately if you are interested. * Dear all, We invite applications for PhD study at the University of Birmingham. We are a group of (mostly) theoretical computer scientists who explore fundamental concepts in computation. Our work includes category theory, computational complexity, programming language semantics, proof theory, type theory, verification and much else besides. See our webpage, with links to individual researchers, here: https://www.birmingham.ac.uk/research/activity/computer-science/theory-of-c… Information about PhD applications may be found here: https://www.birmingham.ac.uk/schools/computer-science/postgraduate-research… If you are considering applying, please contact any of us. We will be very happy to discuss the opportunities available. Best regards, The Birmingham CS theory group, including:- Benedikt Ahrens Rajesh Chitnis Anupam Das Martín Escardó Eric Finster Dan Ghica Mirco Giacobbe Paul Levy Sonia Marin Sean Moss Jakub Opršal Vincent Rahli Uday Reddy Eike Ritter You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 1

Re: "First" use of 'Category theory' to describe our field
by David Roberts 23 Feb '24

23 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/ ]

3 4

Fibrewise opposite fibration
by David Roberts 10 Feb '24

10 Feb '24

Hi all what with all the discussion of Bénabou and fibrations, I have a question about what happens at a foundational level when one takes the opposite of a fibration E --> B fibrewise. Call this (E/B)^op --> B For reference, one can see section 5 of Streicher's https://arxiv.org/abs/1801.02927 for the construction. The point is that the morphisms are defined to be equivalence classes of certain data. However, in a setting where one cannot necessarily form equivalence classes, it's less clear how to proceed. The point is that I don't want to be assuming any particular foundations here, just working at the level of a first-order theory (in the way that ETCS is a first-order theory of sets, say) The only thing I can think of is that the construction actually describes a category weakly enriched in 0-truncated groupoids (or whatever you want to call the first-order description of such a thing). You still get a functor down to the base 1-category, and perhaps one has to now think about what it means for such a thing to be a fibration, without passing to the plan 1-category quotient. That is probably fine for my purposes, but then you have to worry that taking the fibrewise opposite again should return the original fibration, at least up to equivalence. The original construction with the equivalence classes gives back the original thing up to *isomorphism*: ((E/B)^op/B)^op \simeq E, over B. So now one has to think about what the fiberwise opposite construction looks like for these slightly generalised fibrations (enriched with 0-truncated groupoids), and one would hope that this gives back the original thing after two applications (again, up to the appropriate notion of equivalence). Note that the construction in the literature (eg Streicher's notes, or Jacob's book) has the fibres (E/B)^op_b of the fibrewise opposite be *isomorphic* to the opposite of the original fibres E_b. In this fancier setting, one might also only get equivalence, but I haven't checked that. Has anyone thought about something like this before? Or any pointers to anything related? Best wishes, David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

7 11

Re: Sorry
by Dusko Pavlovic 08 Feb '24

08 Feb '24

i did, of course, miss something (as i suspected before hitting return, but didn't resist :) but it seems that fixing the error makes the benabou/lawvere link even nicer. (even if i am still missing something i am sure that the link is there.) the one-to-one correspondence between definable subfibrations of E---->B and the "comprehensions" E---->Sub(B) stands. the claim that the subfibration C---->B is obtained by pullback is wrong, because we don't want to pull back along the "truth" into Sub(B) but along the "comprehension". remember how lawvere defined comprehension of the bifibration E---->B to be (in equivalent to hyperdoctrines) the right adjoint of the cartesian functor Arr(B)---->E mapping (i--f-->j) to f_!(top_i). [[i even introduced Arr(B) in the previous message but oversimplified and didn't use it.]] now i can of course restrict that functor to Sub(B)---->E. a definable subfibration C of E, determines a right adjoint E---->Sub(B) and the adjunction localizes on C. how can i say this for fibrations, without using the direct images? well (now i write Arr(E) as E/E and B/P is the comma into P) E--P-->B is a fibration if and only if the induced functor E/E---->B/P is a reflection (the cartesian liftings induce a right adjoint right splitting). a subcategory C of E is a definable subfibration of P if and only E/E---->B/P restricts to C/E---->Sub/P. i think. apologies that i am thinking so much in public, but there is no shortage of private thinking and there is a shortage of public thinking and we should all think together how to bring lawvere and benabou together :) -- dusko On Mon, Jan 22, 2024 at 3:05 PM Dusko Pavlovic <duskgoo(a)gmail.com> wrote: > as we are talking about lawvere's and benabou's nachlasse, it occurred to > me to ask what would benabou's definability be in lawvere's terms. maybe > they both knew this and maybe other people do, but i hope it doesn't hurt > to spell it out. > > let B be a category with pullbacks so we have the fibrations > Arr(B)--Cod-->B and > Sub(B)--Cod-->B, > where Arr(B) is the category of arrows and Sub(B) is the category of > subobjects. the cartesian functors B>--Ids-->Sub(B) and B>--Ids-->Arr(B) > are the right adjoints. > > Prop. B>--Ids-->Sub(B) is the classifier of definable subfibrations. more > precisely, for any fibration E--P-->B and a subfibration C>---->E here is a > unique cartesian functor E--c-->Sub(B) such that the fibration C---->B is > the pullback of c along B>--Ids-->Sub(B). > > i did check this, but i didn't check it twice, so i may still be missing > something. > > -- dusko > > On Mon, Jan 22, 2024 at 10:00 AM Francis Borceux < > francis.borceux(a)uclouvain.be> wrote: > >> >> Sorry, and thanks to Jon for noticing the slip of terminology in my mail. >> >> Indeed, Bénabou was insisting on the importance of his notion of >> definability. >> >> Francis >> >> *********************************** >> Francis Borceux >> 6 rue François >> 1490 Court-Saint-Étienne >> Belgique >> Fixe: +32(0)10614205 >> Mobile: +32(0)478390328 >> >> >> ---------- >> >> You're receiving this message because you're a member of the Categories >> mailing list group from Macquarie University. >> >> Leave group: >> >> https://protect-au.mimecast.com/s/JhEqC5QP8ySGq6xkfzFqDC?domain=outlook.off… >> >

3 3

Re: Fibrewise opposite fibration
by streicher＠mathematik.tu-darmstadt.de 01 Feb '24

01 Feb '24

If we work with split fibrations and arbitrary cartesian functors between them we can construct the opposite of a fibration without quotienting. That is possible but in my eyes less elegant than the usual approach where one assumes that one can factorize modulo equivalence relations even if they are big. Thomas ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…

5 6

SUBJECT: Last Call (deadline Jan 31): School of Formalized Mathematics (May 13 - 17, 2024)
by Valeria de Paiva 30 Jan '24

30 Jan '24

The Hausdorff Trimester "Prospects of Formalized Mathematics" will organize a "School of Formalized Mathematics" (May 13 - 17, 2024). This is targeted towards junior research ers and Mathematicans with little prior exposure to Formalization and Automated Theorem Proving and any who are interested in this technology. Prospective participants can still apply at [1] DEADLINE: Jan. 31. 2024 (CET). At the school the major theorem proving systems and libraries are introduced by their developers. We envision it to be quite informal, hands-on, and interactive. We plan to have plenary sessions in the mornings 9-11 on Monday May 13 to introduce the systems in a ca. 20 min lightning talks, and in the remaining days present specific aspects of general interest of the systems (please volunteer two topics) in 40 min presentations. In the afternoons we will form small groups that get their hands dirty in specific formalization projects. [1] https://him-application.uni-bonn.de/index.php?id=5960 [2] https://www.mathematics.uni-bonn.de/him/news-him/graduate-colloquium-luise-… [https://mail.google.com/mail/u/0/images/cleardot.gif] -- Valeria de Paiva http://vcvpaiva.github.io/ https://topos.institute/ http://www.cs.bham.ac.uk/~vdp/ You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

*Extended Deadline* 17th International Workshop on Coalgebraic Methods in Computer Science (CMCS'24)
by Urbat, Henning 30 Jan '24

30 Jan '24

The submission deadline for the 17th International Workshop on Coalgebraic Methods in Computer Science (CMCS'24) has been extended to **5 February 2024** (abstracts) and **8 February 2024** (papers). Please find below the updated Call for Papers: FINAL CALL FOR PAPERS (UPDATE) ============================== The 17th IFIP WG 1.3 International Workshop on Coalgebraic Methods in Computer Science (CMCS'24) Luxembourg, 6-7 April 2024 (co-located with ETAPS 2024) https://www.coalg.org/cmcs24/ 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 are the theory and applications of coalgebra and coinductive reasoning in all research areas of Computer Science, including (but not limited to) the following: - set-theoretic and categorical foundations of coalgebra; - algebra & coalgebra, (co)monads, and distributive laws; - (modal) logic; - automata theory and formal languages; - coinductive definitions and proof principles (including "up-to" techniques) - semantic models of computation (for programming languages, dynamical systems, term rewriting, etc.) - functional, objected-oriented, concurrent, and constraint programming; - type theory (notably behavioural typing); - formal verification and specification; - control theory (notably discrete events and hybrid systems); - quantum computing; - game theory; - implementation, tools, and proof assistants In addition to presentations of contributed papers, the workshop will also include invited talks and tutorials. Venue and event --------------- CMCS '24 will be held in Luxembourg City, Luxembourg, co-located with ETAPS 2024 on 6-7 April 2024. Important dates (Anywhere On Earth) ----------------------------------- Abstract regular papers 5 February 2024 Submission regular papers 8 February 2024 Notification regular papers 11 March 2024 Final version 1 April 2024 Submission short contributions 7 March 2024 Notification short contributions 11 March 2024 Programme committee ------------------- Adriana Balan (University Politehnica of Bucharest, Romania) Harsh Beohar (University of Sheffield, United Kingdom) Marta Bilkova (Academy of Sciences of the Czech Republic) Fredrik Dahlqvist (Queen Mary University of London, United Kingdom) Jérémy Dubut (National Institute of Advanced Industrial Science and Technology, Japan) Sebastian Enqvist (Lund University, Sweden) Richard Garner (Macquarie University, Australia) Ichiro Hasuo (National Institute of Informatics, Japan) Tobias Kappé (Open University of the Netherlands and ILLC, University of Amsterdam) Marina Lenisa (University of Udine, Italy) Larry Moss (Indiana University Bloomington, United States) Fredrik Nordvall Forsberg (University of Strathclyde, United Kingdom) Jurriaan Rot (Radboud University, The Netherlands) Matteo Sammartino (Royal Holloway University of London, United Kingdom) Pawel Sobocinski (Tallinn University of Technology, Estonia) David Spivak (Topos Institute, United States) Sam Staton (University of Oxford, United Kingdom) Tarmo Uustalu (Reykjavik University, Iceland, and Tallinn University of Technology, Estonia) Thorsten Wißmann (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany) PC co-chairs -------------- Barbara König (Universität Duisburg-Essen, Germany) Henning Urbat (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany) Publicity chair --------------- Thorsten Wißmann (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany) Steering committee ------------------ Corina Cirstea, University of Southampton, United Kingdom Helle Hansen, University of Groningen, The Netherlands Ichiro Hasuo, National Institute of Informatics, Japan Bart Jacobs, Radboud University Nijmegen, The Netherlands Stefan Milius, Friedrich-Alexander Universität Erlangen-Nürnberg, Germany Daniela Petrişan, IRIF, Université Paris-Cité, France Jurriaan Rot, Radboud University Nijmegen, The Netherlands Lutz Schröder, Friedrich-Alexander Universität Erlangen-Nürnberg, Germany Alexandra Silva (chair), Cornell University, United States Fabio Zanasi (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. Regular papers should be at most 18 pages long in Springer LNCS style, excluding references. A clearly marked appendix containing technical proofs can be added, but this will not be published in the proceedings. Note that the reviewers are not obliged to read the appendix, and the merits of the paper should be clear from the main text. 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 including references. Regular papers and short contributions must be submitted electronically as a PDF file via the Easychair system at https://easychair.org/my/conference?conf=cmcs2024 The proceedings of CMCS 2024 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. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>

1 0

Robin Cockett Doctor Honoris Causa of Tallinn UT
by Tarmo Uustalu 29 Jan '24

29 Jan '24

Hello Categories, I thought it should be appropriate to share the news here. The Senate of the Tallinn U of Technology has on 23 Jan 2024 decided to bestow on the U of Calgary professor J. Robin B. Cockett the title of Doctor Honoris Causa of the university. This is for his contributions to advancing the study of mathematical foundations of algorithmics and programming in Tallinn. I am very happy for this distinction to Robin, who we have been privileged to have as a teacher and friend for a long time (25 years!). Robin's shining passion for his subject and his uncompromising thoroughness have been particularly inspiring. I am also very pleased to have our field spotlighted at this university on this occasion; it is no small thing for us. Tarmo U ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as…

7 6

Hiring at Western Sydney University
by Richard Garner 28 Jan '24

28 Jan '24

Dear all, I have nothing to do with this but thought it could be of interest to some here. Western Sydney University are hiring: https://uws.nga.net.au/?jati=18075E26-931D-895E-139D-D1EBAAD4ED33 This is a permanent position at Level B, which is equivalent to UK lecturer or US assistant professor. The maths department at WSU is small but friendly, and while they don't have any category theorists per se, there are a couple of quite category-theoretic people there: James East who works on semigroups and combinatorially defined free categories, and Roozbeh Hazrat who works on inter alia Leavitt path algebras. You would also be a short hop across town from us here at Macquarie. You should not contact me about this position because I have no hand in it! The specified contact is: A/Prof Volker Gebhardt via v.gebhardt(a)westernsydney.edu.au <mailto:v.gebhardt@westernsydney.edu.au> Hope this is of interest to some! Richard

1 0