You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
JS PL (he/him) (Dec 08 2025 at 09:13):The Pacific Category Theory (PCT) seminar is a new online seminar for the category theory community in the Asia-Pacific time zone and beyond.
It will run once or twice a month on Fridays at 10am JST/12pm AED (1am UTC).
The first talk will be given by Richard Garner (Macquarie University) on
Title: Universal enrichments
Abstract: For a given category C, there are all sorts of things we might enrich it in. For example, the category of complex vector spaces can be enriched in commutative monoids, or abelian groups, or real vector spaces, or complex vector spaces. In this talk, we explain how, for any locally presentable category C, there is a universal locally presentable monoidal category V in which it can be enriched. The fun part is trying to calculate V for particular choices of C; in general, it is rather intractable but sometimes we get lucky!
The zoom link will be posted on the website https://pctseminar.github.io/ shortly before the talk.
Kevin Carlson (Dec 08 2025 at 18:41):This looks great! Is the late Zoom link posting a one-time-only thing? It's a bit inconvenient to have a calendar item that just contains the instructions to navigate to a GitHub and poke around for a Zoom link, as opposed to having the link right in the event.
JS PL (he/him) (Dec 11 2025 at 23:44):Reminder about the first PCT talk by Richard Garner in a little over an hour at , here is the zoom link: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1 (also on the website https://pctseminar.github.io/) join us if you're interested!
JS PL (he/him) (Dec 11 2025 at 23:45):Kevin Carlson said:
This looks great! Is the late Zoom link posting a one-time-only thing? It's a bit inconvenient to have a calendar item that just contains the instructions to navigate to a GitHub and poke around for a Zoom link, as opposed to having the link right in the event.
Fair point : still ironing out the details and setup. Will bring it up with the others. Thanks!
Jack Jia (Dec 12 2025 at 00:19):How long are the talks? I can't find any information on the website.
JS PL (he/him) (Dec 12 2025 at 00:25):Jack Jia said:
How long are the talks? I can't find any information on the website.
45-60 minutes
JS PL (he/him) (Jan 11 2026 at 21:12):We also have a youtube channel where we will be posting the talks: https://www.youtube.com/channel/UCdHnpEqXvvvYw16Cg_L6O3g
JS PL (he/him) (Jan 12 2026 at 05:43):Taichi Uemura will give a talk for the second session of the PCT seminar
(<https://pctseminar.github.io/>) on Friday January 16 at 10am JST/12pm AED
(1am UTC).
The zoom link to join the seminar is here:
<https://kyoto-u-
edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1>
Title: A direct-categorical approach to opetopic sets and opetopes
Abstract: Opetopes and opetopic sets were introduced by Baez and Dolan as
a combinatorial approach to weak ω-categories. Since its birth,
several equivalent definitions have been proposed. Recently, Leclerc gave
a posetal definition of opetopes, where an opetope is encoded as a poset
of cells ordered by the subcell relation. This seems to be the most
elementary and simple definition of opetopes, but there is some
complication related to loops. In this talk, I propose another elementary
definition of opetopes, encoding an opetope as a direct category rather
than a poset. Loop issues are resolved by allowing distinct parallel
morphisms, and the theory of opetopic sets gets simplified.
We hope to see you there!
JS PL (he/him) (Jan 16 2026 at 00:07):Reminder about the second PCT talk by Taichi Uemura in a little under an hour at , here is the zoom link: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1 (also on the website https://pctseminar.github.io/) join us if you're interested!
JS PL (he/him) (Feb 24 2026 at 03:14):Yuki Imamura will give a talk for the third session of the PCT seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is here: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: A formal category theoretic approach to the homotopy theory of dg categories
Abstract: A dg category is a category enriched over the category of complexes of modules. Arising from the homotopy theory of complexes up to quasi-isomorphism, dg categories admit a natural homotopy theory in their own right, in which the weak equivalences are the quasi-equivalences. In this talk, I present an approach to the homotopy theory of dg categories from the viewpoint of formal category theory. Concretely, I construct a proarrow equipment in the sense of Wood that captures the homotopy theory of dg categories, and study the behavior of homotopy limits in dg categories within this framework.
We hope to see you there!
JS PL (he/him) (Feb 26 2026 at 22:13):Reminder about today’s talk, join us if you are interested!
JS PL (he/him) (Mar 19 2026 at 22:00):Rose Kudzman-Blais will give a talk for this month's PCT seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is here: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: (Bi)categorical Semantics for Non-Commutative Linear Logic
Abstract: Girard introduced a sub-structural logic, without contraction and weakening, in 1987 known as linear logic. Linear logic was initially introduced as a commutative logic, however its sophisticated structural rules allowed the further introduction of non-commutative variants. Of note are Lambek’s classical bilinear logic and Yetter’s cyclic linear logic. Both are non-commutative variants of multiplicative linear logic, wherein tensor and par are non-commutative connectives, but the former considers right and left versions of linear negation, while the latter has only one coherent version. In this talk, we shall consider both these variants and do a deep dive into their categorical and bicategorical semantics as developed by authors Barr, Cockett, Kowslowski and Seely over the years.
We hope to see you there!
JS PL (he/him) (Apr 19 2026 at 23:14):Dusko Pavlovic (University of Hawaii) will give a talk for this month's PCT seminar (https://pctseminar.github.io/) on Friday April 24 at
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: From concept mining to categorical nuclei and tight completions
Abstract:
While students learn from teachers and textbooks, machines learn from datasets crawled on the web. Either way, the concepts arise as invariants of the matrices of term-situation contexts. The process of learning is therefore construed as an instance of spectral decomposition through nuclear spaces of latent concepts. When the data are not just counted and averaged, but stored as data sets, the matrix entries are not numbers but sets. The induced matrices of sets form profunctors (distributors) under the actions of the categories of previously mined concepts. This gives rise to the task of spectral decomposition of profunctors, and the quest for the induced nuclear adjunctions. Some special cases are well-known and widely used. The Formal Concept Analysis (FCA) mines concepts from relational and posetal contexts. Latent Semantic Analysis (LSA) mines the latent concepts from given numeric contexts, capturing the cumulative correlations as bimodules. The family of linear concept analysis algorithms is among the most run on the web, since it underlies all personalized recommendation and profiling systems. The feedback loops inherent in such systems cause the information cascades and the dreaded "echo chambers”. The engineering mitigations led to the context matrices of sets and suggested the construction of the categorical nucleus, which reopened and answered a long abandoned fundamental question. This presentation includes work driven by ongoing collaborations with Dominic Hughes.
We hope to see you there!
JS PL (he/him) (Apr 24 2026 at 00:59):Reminder about today's talk starting in a few minutes.
JS PL (he/him) (Apr 30 2026 at 22:20):Ross Street (Macquarie University) will give this month's online PCT seminar (https://pctseminar.github.io/) talk on
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: Homodular pseudofunctors as objective invariants
Abstract:
As Riemann proved, a lot can come out of an 8 page paper! There are two techniques used in the paper [André Joyal, Calcul intégral combinatoire et homologie des groupes symétriques, C.R. Acad. Sci. Canada VII(6) (Dec. 1985) 337--342] which fascinate me. The author's goal is to prove something about how the homology of the symmetric group on n symbols sits in that on n+1 symbols. Rather than specify a particular homological functor, his first technique is to construct a universal one and prove the result for that. The property in question is preserved by additive functors and so holds for any homology. The second technique is to use his theory of (virtual) species of structure where passing from n to n+1 gives differentiation. My goal is to do something similar for the general linear groups over a fixed finite field. I have begun the adaptation of the two techniques and hope the results so far will be of independent interest. The two strands have yet to conflow into the desired application.
We hope to see you there!
Also reminder that recorded talks are posted afterwards on the seminar's youtube channel:
https://www.youtube.com/@PCTSeminar