June 2026 - Categories - categories.org.au

Reference for the analytic vs. synthetic distinction in mathematics
by José Manuel Rodríguez Caballero 27 Jul '26

27 Jul '26

Dear all, I would like to include the following distinction in a manuscript: There are two styles of reasoning in mathematics: 1. *analytic*: structures built from a “point-set” substrate; 2. *synthetic*: axioms imposed directly on the available types. At present, the only source I have found stating this distinction in this form is the nLab page on synthetic mathematics ( https://ncatlab.org/nlab/show/synthetic+mathematics ). Could anyone point me to a published reference where this terminology or this formulation of the analytic vs. synthetic approaches is explicitly discussed? Many thanks in advance. Best regards, JMRC

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Did you see this characterisation of Z in the 70s?
by David Roberts 08 Jul '26

08 Jul '26

Hi all, I'm requiring the brains trust of the older generation to let me know if the following definition (as exactly like this as possible) was in the air or written down pre-1980. I will assume C is a cartesian closed category, but perhaps it was stated for C a topos at the time. Definition: Let C be a cartesian closed category. An _integers object_ is a pointed object 0 : 1 --> Z with the data s : Z ---> Z and p : Z ---> Z such that p = s^{-1}, and is the initial among pointed objects with an automorphism. I have found this definition published in a computer science paper: * Turner, D.A. (1985). Miranda: A non-strict functional language with polymorphic types. In: Jouannaud, JP. (eds) Functional Programming Languages and Computer Architecture. FPCA 1985. Lecture Notes in Computer Science, vol 201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15975-4_26 and something very similar in papers in 1982 and 1980 coming from the ADJ school of computer science (heavily influenced by category theory). There it's stated more in terms of giving the definition of a algebraic data type in some inductive means. But I can't find it in the category theory literature proper. I don't know if it came from some old logic/set theory paper, or was from CT, or was just first written down by computer scientists, but it was so incredibly obvious no one wrote it down in mathematics. Please note that "well the definition is obvious" _now_ is not really sufficient, I'd like to hear from someone from pre-1980 who can say "I recall discussing this definition at the time and it was so obvious then that no one wrote it down" if this is the type of answer I'm going to get. Moreover, since I'm interested in the case where I can't assume I have colimits, any early mention _constructing_ an object of integers from the NNO in a topos in "the usual way" also isn't useful (what colimits does a CCC have for free? Certainly not quotients or pushouts) More recently (in the last decade) this characteristion has been used in MLTT/Homotopy Type Theory, and this being written on the nLab in a purely categorical way is what alerted me to the characterisation. I'm hoping to get a reference to add there, aside from the computer science ones which strike me as very likely influenced by something a category theorist could have written down. Thanks in advance, David -- Dr David Roberts http://ncatlab.org/nlab/show/David+Roberts Adjunct Associate Lecturer School of Mathematical Sciences Adelaide University — Tirkangkaku SA 5005 AUSTRALIA Australian University Provider Number PRV14404 CRICOS Provider Number 04249J ----------------------------------------------------- IMPORTANT: This email may be privileged and/or confidential, and the sender does not waive any related rights and obligations. Any distribution, use or copying of this email or the information it contains by other than an intended recipient is unauthorised. If you receive this email in error, please advise me (by return email or otherwise) immediately.

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Terminology for locally cartesian closed categories, with and without a terminal object
by Emily Riehl 30 Jun '26

30 Jun '26

There has been some discussion on the Category Theory zulip about the proper terminology for locally cartesian closed categories that I’d like to extend to the broader community. https://categorytheory.zulipchat.com/#narrow/channel/229136-theory.3A-categ… I raised this question because I have added a new section on locally cartesian closed categories as part of a revised second edition of Category Theory in Context. The current draft, can be found here and comments on this or anything else are very welcome (especially before the end of August, with sooner better than later): https://emilyriehl.github.io/files/context.pdf Does the community prefer reserving the term “locally cartesian closed categories” for the case where a terminal object exists (in addition to pullbacks)? If so, is there a good name for the version that is missing the terminal object? If not, is there a good name for the version that has a final limits? As pointed out on the chat (h/t Nathanael Arkor) both conventions are widely used in the literature. Thanks, Emily PS: I was personally persuaded of the utility of the more general notion by the example of sets and monomorphisms. In the current draft of the text, I’m trying to provide intuition for some of the connections to logic without explicitly mentioning dependent type theory. -- Kelly Miller Professor of Mathematics (she/her) Johns Hopkins University emilyriehl.github.io

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New Issue of the Cahiers (2nd quarter 2026)
by Marino Gran 29 Jun '26

29 Jun '26

Dear Colleagues, We are pleased to inform you that the new issue of the Cahiers (Volume LXVII, 2nd quarter 2026) is now freely available for download from the Cahiers website: https://cahierstgdc.com<https://url.au.m.mimecastprotect.com/s/lL9ECjZ12RfnKQrOOUWfPTm6lJ4?domain=c…> This special issue is dedicated to the memory of Marek Zawadowski. We would like to thank Pierre-Louis Curien, Silvio Ghilardi, Martin Hyland, Krzysztof Kapulkin, Jaap van Oosten, Karol Szumiło and Clemens Berger for their contributions to the preparation of this special issue. With best regards, Andrée Ehresmann, René Guitart, Isar Stubbe and Marino Gran

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Workshop in celebration of Marcelo Fiore's 60th birthday (online attendance)
by Nathanael Arkor 28 Jun '26

28 Jun '26

Dear all, We are happy to announce that the workshop in celebration of Marcelo Fiore's 60th birthday (2nd – 3rd of July) will be streamed online, so that those who are unable to attend in person can still participate. We will add a streaming link to the website, where you can already find the workshop schedule, shortly before the workshop begins: https://fiorefest.gitlab.io/home Best wishes, Nathanael, Vikraman and Zeinab

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Call for Participation and Talk Proposals - Categorical Applications and Foundations Exchange in Tallinn, Estonia
by Mario Román García 24 Jun '26

24 Jun '26

Dear colleagues, We are pleased to invite you to join us for a two-day workshop at the School of Information Technologies in Tallinn, Estonia. Registration is free but required, as the capacity of the venue is limited. Details are available on the webpage for the event. CAFÉ 2026 - Tallinn, Estonia. Categorical Applications and Foundations Exchange. 13-14th July 2026. Webpage: https://categories-applications-and-foundations.github.io/cafe2026/ The Categorical Applications and Foundations Exchange (CAFÉ) is a workshop bridging theoretical and applied topics in category theory. CAFÉ 2026 will be hosted in Tallinn on the 13th and 14th of July, and it aims to foster collaboration and community discussion. It invites participation and talk proposals of around 30 minutes on category theory, both foundations and applications, in a broad sense. Registration deadline: June 30, 2026 (AoE, may be extended). Notification: July 3, 2026. Workshop: July 13-14, 2026. Best regards, The organizers, Bryce Clarke, Alessandro Di Giorgio, Elena Di Lavore, Fosco Loregian, and Mario Román.

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PhD position in Categorical Methods in Computer Science - Tallinn University of Technology
by Mario Román García 24 Jun '26

24 Jun '26

Dear colleagues, I am advertising a PhD position in categorical methods in computer science at Tallinn University of Technology, jointly supervised by Paweł Sobociński<https://www.compose.ee/pawel/> and me (Mario Román<https://www.marioroman.xyz/>). The duration of the PhD programme is 4 years, with a gross monthly salary of 2300€. The deadline for applications is on the 12th of July 2026. Applications can be submitted via the following link. - https://taltech.teamdash.com/p/job/RFey8aBC/early-stage-researcher-phd-posi… The Compositional Systems and Methods group<https://compose.ee/> at Tallinn University of Technology is a lively, welcoming and diverse group working on different topics across theoretical computer science and sharing a common interest in categorical methods. We work closely with the Logic and Semantics group<https://cs.ioc.ee/lsg/> in the same University. Tallinn University of Technology, and our group in particular, remains committed to equality, diversity and inclusion; we particularly encourage members of discriminated minorities to apply. Please do not hesitate to contact us for any questions or more information. Best regards, Mario

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Category Theory under threat in Cambridge
by P.T. Johnstone 12 Jun '26

12 Jun '26

As many subscribers to this list will know, I have continued to lecture a course on Category Theory in Part III of the Mathematical Tripos in Cambridge every year since Martin Hyland and I retired (there being no-one on the current Faculty who is able to do it). I'm quite proud of the fact that I didn't even miss a year as a result of Covid! I have now been informed that Cambridge University has a new policy of not allowing people who are not on the University payroll to teach examinable courses, which if implemented strictly means that Category Theory will cease to be an option in Part III from next year. I know that there are many people on this list who first encountered categories through Martin's or my Part III lectures. If you feel, as I do, that the suppression of this option is a disgrace to Cambridge, I'd be grateful if you could write to the Head of DPMMS, Ivan Smith (is200(a)cam.ac.uk) and tell him so. Peter Johnstone

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ItaCa Fest - 16th of June
by Giacomo Tendas 12 Jun '26

12 Jun '26

Dear all, ItaCa Fest 2026 continues on Tuesday the 16th of June. We will start at 3:00 PM (Italian time) as usual. Here is the list of speakers for this episode: • M. Spadetto – *A conservativity proof strategy via 2-category theory*; • L. Ye – *The pro-étale site for first-order logic*; • G. Boccali – *Normalization for (co-)lax-idempotent 2-sketches*. You can find a precise schedule, the abstracts, and the Zoom link at the following page: https://progetto-itaca.github.io/fests/fest26.html Best wishes, Giacomo (On behalf of the Scientific Committee)

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Expressions of Interest for fellowships with the MSP group, University of Strathclyde, Scotland
by Fredrik Nordvall Forsberg 10 Jun '26

10 Jun '26

Dear colleagues, The Mathematically Structured Programming (MSP) group at the University of Strathclyde, Glasgow, Scotland, invites expressions of interest from candidates who would like to apply for the following fellowship schemes with us as the host institution: 1. MSCA Postdoctoral Fellowships 2026 (deadline: 9 September 2026) https://marie-sklodowska-curie-actions.ec.europa.eu/actions/postdoctoral-fe… 2. EPSRC Mathematical Sciences Early Independence Fellowships (next batch deadline: 30 September 2026) https://www.ukri.org/opportunity/mathematical-sciences-early-independence-f… Please see the links above for full details on *eligibility* and the *application process*. == About the MSP Group == Our vision is to use mathematics to understand the nature of computation, and to turn that understanding into the next generation of programming languages. We see the mathematical foundations of computation and programming as inextricably linked --- we study one so as to develop the other. The group has 8 (soon to be 9) academic staff, and a lively community of PhD students. More about our research and members is available here: https://msp.cis.strath.ac.uk/people.html == Get in Touch == If you’re interested, please drop an email to any of us, with a few words about your research interests and which scheme you have in mind. We’re happy to discuss project ideas and help you with the application, and the application process. There is also institutional support from the university for preparing the same. Please contact us as soon as possible, but ideally at least two months before the deadline. Also, please feel free to forward this to anyone who might be interested. Best wishes, Fredrik Nordvall Forsberg

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