February 2024 - Categories - categories.org.au

Lecture notes by Bill Lawvere
by Michael Barr, Prof. 23 Apr '26

23 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>

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PhD opportunities at the University of Birmingham
by Paul Levy 25 Nov '24

25 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>

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MFPS 2024: final CFP
by Alex Simpson 01 Mar '24

01 Mar '24

A final CFP for MFPS 2024, with new information on invited speakers, special sessions and the pc. Submission deadline 29th March. --- # MFPS XL: Mathematical Foundations of Programming Semantics ## Call for papers The 40th Conference on the Mathematical Foundations of Programming Semantics (MFPS XL) takes place at the University of Oxford, UK, from 19-21 June 2024, where it will be colocated with the 7th International Conference on Applied Category Theory (ACT 2024). MFPS conferences are dedicated to the areas of mathematics, logic, and computer science that are related to models of computation in general, and to semantics of programming languages in particular. This is a forum where researchers in computer science and mathematics can meet and exchange ideas. The participation of researchers in neighbouring areas is strongly encouraged. Topics include, but are not limited to, the following: bio-computation; concurrent qualitative and quantitative distributed systems; process calculi; probabilistic systems; constructive mathematics; domain theory and categorical models; formal languages; formal methods; game semantics; lambda calculus; programming-language theory; quantum computation; security; topological models; logic; type systems; type theory. We also welcome contributions that address applications of semantics to novel areas such as complex systems, markets, and networks, for example. Conference home page: [https://oxford24.github.io/](https://oxford24.github.io/) ## SUBMISSION ### Important dates: * March 29: paper submission * May 3: notification of authors * June 3: conference papers ready * June 19–21: conference ### Submissions Submissions should be prepared using the [MFPS macros](https://mfpsconf.org/?page_id=309) in the form of a PDF file. [Submission is via EasyChair](https://easychair.org/conferences/?conf=mfps2024). For the first time at MFPS, there are two submission categories: * regular research contributions, * early announcements. Early announcements are a new feature at MFPS XL. They offer a forum for the early presentation of new scientific contributions without the accompanying technical justification that is expected in a regular research contribution. The page limit for both kinds of submission is 15 pages, excluding bibliography and appendices. However, it is expected that early announcements will typically be much shorter, taking only as many pages as is required to present the announced contribution. Early announcements will be refereed primarily on their potential interest-value to the MFPS audience. Early announcements should be identified by clearly labelling them with "Early Announcement" at the start of the pdf document. Early announcements will be given equal presentation time to regular research contributions at the conference. ### Proceedings A preliminary proceedings will be distributed at the meeting, containing both regular research contributions and early announcements. Final proceedings, containing regular research contributions only, will be published in Electronic Notes in Theoretical Informatics and Computer Science (ENTICS https://entics.episciences.org/) This open-access series is hosted by Episciences.org as an overlay for papers published by the CORR arXiv or HAL. It is planned to publish a journal special issue for selected papers from MFPS XL. ## INVITED SPEAKERS There will be 4 invited speakers. * Philippa Gardner (Imperial College, London, UK) * Ohad Kammar (University of Edinburgh, UK) * Catuscia Palamidessi (INRIA Saclay & LIX, France) * Andrew Pitts (University of Cambridge Emeritus, joint ACT/MFPS plenary speaker) ## SPECIAL SESSIONS There will be 3 special sessions. * Special session in memory of Philip Scott (joint session with ACT, organiser Rick Blute) * Special session on the semantics of non-wellfounded and circular proofs (organisers Anupam Das and Abhishek De) * Special session associated with the invited talk of Philippa Gardner (organiser Philippa Gardner) ## PROGRAMME COMMITTEE: * Danel Ahman (University of Tartu) * Amal Ahmed (Northeastern University) * Sandra Alves (University of Porto) * Paolo Baldan (Università di Padova) * Andrej Bauer (University of Ljubljana) * Lars Birkedal (Aarhus University) * Steve Brookes (Carnegie Mellon University) * Valentina Castiglioni (Eindhoven University of Technology) * Liron Cohen (Ben-Gurion University) * Raphaëlle Crubillé (IRIF) * Valeria De Paiva (Topos Institute, co-chair) * Masahito Hasegawa (Kyoto University) * Justin Hsu (Cornell University) * Patricia Johann (Appalachian State University) * Achim Jung (University of Birmingham) * Marie Kerjean (CNRS, LIPN, Université Sorbonne Paris Nord) * Robbert Krebbers (Radboud University) * Paul Levy (University of Birmingham) * Michael Mislove (Tulane University) * Daniele Nantes-Sobrinho (Imperial College London) * Alex Simpson (University of Ljubljana, co-chair) * Christine Tasson (Sorbonne Université) ## LOCAL ORGANISER: * Sam Staton You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. 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Logic Colloquium 2024, Gothenburg, 24-28 June 2024
by Ivan Di Liberti 28 Feb '24

28 Feb '24

Dear all, the logic group at GU are hosting this year’s Logic Colloquium (the Annual European Summer Meeting of the Association for Symbolic Logic). Appended to this message is the new call for submissions. In summary: + Registration is now open (early registration deadline: 17 April) + Contributed talks deadline is extended to 8 March + Student travel grants deadline is *tomorrow* + Scientific programme is available. We look forward to see you here! ANNOUNCEMENT: Registration open Contributed talks deadline extended Student travel grants deadline approaching Scientific Programme available Logic Colloquium 2024 Gothenburg, Sweden 24-28 June 2024 web: lc2024.se contact: info(a)lc2024.se The Logic Colloquium is the European Summer Meeting of the Association for Symbolic Logic, an annual gathering to present current research in all aspects of logic. In 2024, the meeting will be held 24-28 June at the University of Gothenburg in Sweden. ========================== IMPORTANT DATES ========================== 29 February 2024: Deadline for ASL student travel applications 1 March (extended to 8 March): Deadline for contributed talks 28 March: Notification of student travel grants 2 April: Notification of acceptance of contributed talks 17 April: Early registration deadline 24-28 June: Conference ========================== Scientific Programme ========================== The 2024 meeting will comprise 28 invited talks. In addition, the 2024 Gödel Lecture will be delivered at the meeting. Programme available from https://lc2024.se/program/ Tutorials ========================== - Anuj Dawar, University of Cambridge: Model theory of tame classes of finite structures - Alberto Marcone, Università Di Udine: WQOs and BQOs in logic - Andrei Sipoș, University of Bucharest: An exploration of proof mining Plenary talks ========================== - Daisuke Bekki, Ochanomizu University: From Dependent Types to Natural Language Semantics - Johanna Franklin, Hofstra University: Structural highness notions - James Freitag, University of Illinois at Chicago: When any three solutions are independent - Marianna Girlando, University of Amsterdam: A decision algorithm for intuitionistic S4 - Stephen Jackson, University of North Texas: Recent advances in the combinatorics of determinacy models - Leszek Kołodziejczyk, University of Warsaw: Models of arithmetic that satisfy more collection than induction - Paul-André Melliès, Université Paris Denis Diderot: Recent advances in higher-order automata and profinite lambda-calculus Gödel Lecture ========================== Thomas Scanlon, University of California at Berkeley Special Sessions ========================== Applied Model Theory, chairs: Gareth Jones and Tamara Servi - Vincent Bagayoko, Université Paris Cité - Anna Dmitrieva, University of East Anglia - Adele Padgett, McMaster University Computable Structures, chairs: Uri Andrews and Julia Knight - Meng-Che (Turbo) Ho, California State University - Matthew Harrison-Trainor, University of Illinois - David Gonzalez, University of California, Berkeley Logic, Language and Computation, chairs: Robin Cooper and Stergios Chatzikyriakidis - Kristina Liefke, Ruhr-University, Bochum - Zhaohui Luo, Royal Holloway, University of London - Peter Sutton, Universitat Pompeu Fabra, Barcelona Logic in Philosophy, chairs: Volker Halbach and Heinrich Wansing - Agata Ciabattoni, Technische Universität Wien - Andrzej Indrzejczak, University of Łódź - Johannes Stern, University of Bristol Proof Theory, chairs: Anton Freund and Sonia Marin - Valentin Blot, ENS Paris-Saclay - Lukas Melgaard, University of Birmingham - Takako Nemoto, Tohuku University Set Theory, chairs: Dana Bartošová and Slawomir Solecki - Tamás Kátay, Eötvös Loránd University, Budapest - Claudio Agostini, Technische Universität Wien - Chris Lambie-Hanson, Czech Academy of Sciences ========================== Contributed Talks ========================== The programme committee invites proposals for contributed talks. These can be on published or unpublished work, as well as work in progress. Instructions for submission will be made available through the conference webpage. Abstracts for contributed talks should conform to the Rules for Abstracts of the ASL and papers must be prepared using ASL template and class which is from the conference webpages https://lc2024.se/contributed_talks/ ========================== Programme Committee ========================== Bahareh Afshari (Gothenburg, Sweden) Gal Binyamini (Jerusalem, Israel) Natasha Dobrinen (Notre Dame, USA) Ulrich Kohlenbach (Darmstadt, Germany)(chair) Keng Meng Ng (Singapore) Francesca Poggiolesi (Paris, France) Mehrnoosh Sadrazadeh (London, UK) Reed Solomon (Connecticut, USA) Szymon Toruńczyk (Warsaw, Poland) ========================== Venue ========================== All lectures and talks will take place in Humanisten Building, Renströmsgatan 6, 41255 Göteborg. This is a new and stylish building with all rooms integrated with conference equipment. The venue is 5 minutes from a large transport interchange (Korsvägen) and 15 walk to the centre of Gothenburg. ========================== Registration ========================== Early registration closes on 17 April. Please follow the instructions on the homepage. 3500 SEK Standard 2500 SEK Student ========================== ASL Student travel award ========================== Graduate students and recent PhDs may apply for ASL travel support. Student travel award applications (with accompanying recommendation letters) should be emailed to info(a)lc2024.se no later than February 29, 2024. See the webpage for full instructions. ========================== Local organising committee ========================== Bahareh Afshari (chair), Giacomo Barlucchi, Rasmus Blanck, Gianluca Curzi, Fredrik Engström, Tjeerd Fokkens, Mattias Granberg Olsson, Martin Kaså, Graham E. Leigh, Ivan Di Liberti, Orvar Lorimer Olsson, Dominik Wehr ========================== Sponsors ========================== Association for Symbolic Logic The Royal Society of Arts and Sciences in Gothenburg Knut and Alice Wallenberg Foundation Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg Centre for Linguistic Theory and Studies in Probability, University of Gothenburg ========================== Best, Ivan. —————————————— Ivan Di Liberti Postdoc Göteborgs universitet https://diliberti.github.io 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>

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SYCO 12, Second Call For Papers
by Thibaut Benjamin 27 Feb '24

27 Feb '24

----------------------------------------- CALL FOR SUBMISSIONS TWELFTH SYMPOSIUM ON COMPOSITIONAL STRUCTURES (SYCO 12) Birmingham, UK 15-16 April, 2024 Submission deadline: Monday 11 March 2024 https://www.cl.cam.ac.uk/events/syco/12/ ----------------------------------------- The Symposium on Compositional Structures (SYCO) is an interdisciplinary series of meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in particular where category theory serves as a unifying common language. Previous SYCO events have been held in Palaiseau, Birmingham, Strathclyde, Oxford, Chapman, Leicester, Tallinn, and Como. We welcome submissions from researchers across computer science, mathematics, physics, philosophy, and beyond, with the aim of fostering friendly discussion, disseminating new ideas, and spreading knowledge between fields. Submission is encouraged for both mature research and work in progress, and by both established academics and junior researchers, including students. Submissions is easy, with no formatting or page restrictions. The meeting does not have proceedings, so work can be submitted even if it has been submitted or published elsewhere. You could submit work-in-progress, or a recently completed paper, or even a PhD or Masters thesis. While no list of topics could be exhaustive, SYCO welcomes submissions with a compositional focus related to any of the following areas, in particular from the perspective of category theory: - logical methods in computer science, including classical and quantum programming, type theory, concurrency, natural language processing and machine learning; - graphical calculi, including string diagrams, Petri nets and reaction networks; - languages and frameworks, including process algebras, proof nets, type theory and game semantics; - abstract algebra and pure category theory, including monoidal category theory, higher category theory, operads, polygraphs, and relationships to homotopy theory; - quantum algebra, including quantum computation and representation theory; - tools and techniques, including rewriting, formal proofs and proof assistants, and game theory; - industrial applications, including case studies and real-world problem descriptions. IMPORTANT DATES =============== All deadlines are 23:59 Anywhere on Earth. Submission deadline: Monday 11 March, 2024 Author notification: Monday 18 March, 2024 Symposium dates: Monday 15 and Tuesday 16 April 2024 SUBMISSION INSTRUCTIONS ======================= Submissions are by OpenReview, via the SYCO 12 submission page: https://openreview.net/group?id=cl.cam.ac.uk/SYCO/2024/Symposium (be aware that you will need to create an account on OpenReview, which is automatic if you are using an academic e-mail address, but might take up to 2 weeks with a non-academic e-mail address) Submission is easy, with no format requirements or page restrictions. The meeting does not have proceedings, so work can be submitted even if it has been submitted or published elsewhere. Think creatively: you could submit a recent paper, or notes on work in progress, or even a recent Masters or PhD thesis. In the event that more good-quality submissions are received than can be accommodated in the timetable, the programme committee may choose to *defer* some submissions to a future meeting, rather than reject them. Deferred submissions can be re-submitted to any future SYCO meeting, where they will not need peer review, and where they will be prioritised for inclusion in the programme. Meetings will be held sufficiently frequently to avoid a backlog of deferred papers. If you have a submission which was deferred from a previous SYCO meeting, it will not automatically be considered for SYCO 12; you still need to submit it again through OpenReview. When submitting, append the words "DEFERRED FROM SYCO X" to the title of your paper, replacing "X" with the appropriate meeting number. There is no need to attach any documents. INVITED SPEAKERS ================ Miriam Backens, INRIA Nancy, Graphical rewriting of quantum computations using the ZX-calculus and flow properties Sean Moss, University of Birmingham, TBA PROGRAMME COMMITTEE =================== Todd Ambridge, University of Birmingham Thibaut Benjamin, University of Cambridge (Chair) Olivia Caramello, Univserity of Insubria, Université Paris-Saclay Ross Duncan, University of Strathclyde Chris Heunen, University of Edinburgh Dominic Horsman, University of Grenoble George Kaye, University of Birmingham Aleks Kissinger, University of Oxford Jean-Simon Lemay, Macquarie University Paul Levy, University of Birmingham Samuel Mimram, Ecole Polytechnique Simona Paoli, University of Aberdeen Mehrnoosh Sadrzadeh, University College London Pawel Sobocinski, Tallinn University of Technology Jamie Vicary, University of Cambridge STEERING COMMITTEE ================== Ross Duncan, University of Strathclyde Chris Heunen, University of Edinburgh Dominic Horsman, University of Grenoble Aleks Kissinger, University of Oxford Samuel Mimram, Ecole Polytechnique Simona Paoli, University of Aberdeen Mehrnoosh Sadrzadeh, University College London Pawel Sobocinski, Tallinn University of Technology Jamie Vicary, University of Cambridge You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. 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Re: Fibrewise opposite fibration
by Dusko Pavlovic 26 Feb '24

26 Feb '24

[sorry, i always lag behind.] a global well-order assumption is not a conservative extension even of ZFC. it would make all models of computation extensional. it is also not a conservative extension of the nice non-ZF universes we like these days, including categorical, for basically the same reason. my earlier point was that, since we live among computers, the assumption of local well-ordering seems unavoidable, sooner or later. for the simple reason that all data and code are well-ordered as binaries. but the ordering is not a property, either global or local, but structure. we keep reordering things whenever we write a program. imposing a global ordering structure would require deciding what is what: identifying the intensional and the extensional equality. extensionally :) you are probably right that all this is a sort of a religious war. or maybe not a war, but rather a theological dispute. but note that theologians considered it to be self-evident that they were the bearers of the torch of logical truth. just like we. if we assume that the world is built of sets, like we were taught in math 101, then assuming well-order is indeed questionable in all kinds of ways, burdensome practically, and zermelo's solution to package it behind a big quantifier is a convenient solution. but while discussons whether the world is built of sets as the simplest foundation of everything might be interesting, or not, programmers tend to ignore them and only use sets when pedagogically unavoidable. the reason is that all types in their world are well-ordered AND that transitioning to sets and cardinalities is still as just costly as it was for cantor. so the math that runs in the computers that we use to exchange these messages, discuss foundations, and make calls home, tends to be built on well-ordered types --- which we reorder and reprogram whenever needed. intensionally :) 2c -- dusko On Mon, Feb 12, 2024 at 6:56 PM Nath Rao <khazanarao(a)gmail.com> wrote: > [This no longer about how to define fibrewise opposite fibration, so may > be it is time t change the subject line.] > > IMHO, this seems to be more like a religious war. In "mathematics in the > small", local axiom of choice allows us to choose representatives only > when needed. So we are grew up believing that putting things in the > definition that are not preserved by morphisms is "not done" (the > religious dogma) . But them we run up against issues when we try to do > the same thing in "mathematics in the large", and either ignore the > problem or argue endlessly about how to solve it. > > Also, if are willing to assume that every set comes with a > well-ordering, why not assume a global well-ordering and be done with > it? [If I am going to use universes anyway, it seems to be trivial to do > this, as long as I live inside a fixed universe in any given proof.] For > ZFC, global choice is a conservative extension. Not being a logician, am > not sure, but perhaps it can be shown for global choice is a > conservative extension of local choice of 'all suitable set theories'. > Then we can do global choice with no qualms. > > Regards > Nath Rao > > > > > > ---------- > > You're receiving this message because you're a member of the Categories > mailing list group from Macquarie University. > > Leave group: > > https://url.au.m.mimecastprotect.com/s/IRyOC1WLjwsyM5vLTL23r1?domain=outloo… >

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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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MGS 2024 (Midlands Graduate School)
by Paul Levy 24 Feb '24

24 Feb '24

Dear all, https://www.cs.le.ac.uk/events/mgs2024/ The Midlands Graduate School (MGS) provides an intensive programme of lectures on the Mathematical Foundations of Computing Science. It has run annually since 1999 and has been held at either the University of Birmingham, the University of Leicester, the University of Nottingham, or at the University of Sheffield. The lectures are aimed at postgraduate/PhD students, typically in their first or second year of study for a PhD. However, the school is open to anyone who is interested in learning more about mathematical computing foundations, and all such applicants are warmly welcomed. We very much encourage students from abroad to attend, participants from industry, and many have done so in the past. Celebrating 25 Years, MGS 2024 will be held at the School of Computing and Mathematics, University of Leicester, U.K. The programme includes * Kevin Buzzard (Imperial) as a guest lecturer on the formalisation of mathematics. * Thorsten Altenkirch (Nottingham) on category theory. * Abishek De and Iris van der Giessen (Birmingham) with an introduction to proof theory. * Todd Ambridge (Birmingham) with an introduction to type theory with Agda. * Sonia Marin (Birmingham) on session types. * Ulrik Buchholtz (Nottingham) on synthetic homotopy theory with HoTT/UF. * Reiko Heckel (Leicester) on foundations and applications of graph rewriting. * Tom de Jong (Nottingham) on categorical realisability. Registration is open until 8th March. 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>

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Re: Fibrewise opposite fibration
by Dusko Pavlovic 23 Feb '24

23 Feb '24

sorry, i first lag behind with reading, and then rush with writing before i have read everything that was said. i hope the first paragraph of what i wrote will reawake confusion. it is just a slight variation to what thomas said more precisely. sorry about not reading first :) -- dusko On Tue, Feb 13, 2024 at 9:16 AM Thomas Streicher < streicher(a)mathematik.tu-darmstadt.de> wrote: > Have sorted out off line with Jon Sterling what I meant. > I am working in ZFC together wit the axiom that every set is element > of a Grothendieck universe. So I do not use class choice at all but > instead choice in all Grothendieck universes. > > What I meant is that one should not reduce choice to the first > universe but instead have it for all sets irrespective of the universe > they live in! > > I always found this the most convient setting to work in. But not many > people do it. But if you work in it then there is no need for class > choice anymore. > > Sorry for not having expanded my general implicit assumptions beforehand. > I do see that my view is not the majority view. > > But it is the most convenient setting for doing category theory in my > eyes and it is weaker than real large cardinal axioms that set theorists > study consider. > > Thomas > > > > ---------- > > You're receiving this message because you're a member of the Categories > mailing list group from Macquarie University. > > Leave group: > > https://url.au.m.mimecastprotect.com/s/JYQgCE8wlRCr3MGkHNht4i?domain=outloo… >

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Strong monoidal functors and Day convolution
by Lorenzo Riva 22 Feb '24

22 Feb '24

Dear all, Given a V-enriched category C and sufficiently many assumptions on V and C, there is an equivalence between (symmetric) lax monoidal functors C --> V and (commutative) monoids in Fun(C,V) with respect to Day convolution. I am interested in knowing if there is a similar characterization in the literature for strong monoidal functors, as a property of objects of Mon(Fun(C,V)) or possibly BiMon(Fun(C,V)). The latter contains functors with a monoid structure for Day convolution and a comonoid structure for Day coconvolution, obtained by taking a right Kan extension in place of the usual left Kan extension in the definition of Day convolution. Best, Lorenzo 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>

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