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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
JS PL (he/him) (Jun 01 2026 at 03:36):Thomas Seiller (CNRS) will give a talk for this month's PCT seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: From Statistical Data to Geometry and Logic via Isbell Nuclei
Abstract:
The impressive results obtained by generative language models suggest that statistical information contained in a sufficiently large corpus can be used to recover significant linguistic structure. In particular, Levy and Goldberg (2014) showed that word embeddings can be recovered from low-rank factorisations of word co-occurrence matrices, as obtained in practice through singular value decomposition. While this provides an important first step towards understanding mathematically the structure exploited by language models, it remains limited, notably in its treatment of compositionality.
In this talk I will present a categorical refinement of this perspective, drawing on enriched category theory and realisability methods for linear logic. Starting from a real-valued measure (M:C\times D\to\mathbb R), one studies the Isbell nucleus of the induced enriched adjunction. This construction simultaneously generalises classical formal concepts defined from binary relations and singular value decomposition of linear operators.
While every nucleus carries a canonical lattice structure, in the statistical setting this is only part of a considerably richer picture. On the one hand, the nucleus admits a tropical geometric structure, with row and column spaces appearing as dual presentations of the same object, equipped with a canonical projective metric and polyhedral decomposition. On the other hand, when the underlying data is additionally equipped with concatenation, it carries a type-theoretic structure arising from linear realisability and closely related to substructural logics.
We hope to see you there!
JS PL (he/him) (Jun 05 2026 at 00:58):Reminder about today's talk starting in a few minutes.
JS PL (he/him) (Jul 06 2026 at 07:38):Lili Shen (Sichuan University) will give a talk for this month's PCT
seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: Towards the categorical foundation of quantale-valued sets
Abstract: A classical set may be regarded as a set equipped with an
equality relation valued in the two-element Boolean algebra. Fourman and
Scott generalized this idea by introducing Ω-sets, where equality is
valued in a frame Ω; this construction is closely related to sheaves and
topos theory. Höhle and his collaborators later developed the theory of
quantale-valued sets, replacing the frame Ω by a quantale Q.
This talk provides an overview of the theory of quantale-valued sets and
the ongoing efforts to establish its categorical foundation. I will
explain why Q-sets form a natural and interesting generalization of
Fourman–Scott Ω-sets, and then present two recent results that clarify
the extent to which the category of Q-sets behaves like the category of
sets or the category of Ω-sets. First, for a commutative and divisible
quantale Q, the category of Q-sets is a topos if and only if Q is a frame.
Second, for the unit interval [0,1] equipped with a continuous t-norm *,
the category of ([0,1], *)-sets is cartesian closed if and only if * is
the minimum t-norm.
We hope to see you there!
JS PL (he/him) (Jul 10 2026 at 00:45):Reminder about today's online seminar talk starting soon at
Valeria de Paiva (Jul 12 2026 at 10:58):@JS PL (he/him) were the slides made available?
Nathanael Arkor (Jul 12 2026 at 14:24):There is a recording and slides.
JS PL (he/him) (Jul 12 2026 at 21:08):Valeria de Paiva said:
JS PL (he/him) were the slides made available?
Yes, see Nathanael's answer or it's on the seminar web page: https://pctseminar.github.io/
Valeria de Paiva (Jul 12 2026 at 21:51):Thanks to both of you!
JS PL (he/him) (Jul 30 2026 at 22:00):Sveta Makarova (ANU) will give a talk for this month's PCT seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: Contractions and flops via moduli of non-pure sheaves
Abstract: The goal of the talk is to convince the audience that 2-categorical enhancements of some classical geometric objects yield interesting geometric constructions. Consider the stack of ideal sheaves of l points on a smooth projective variety X. Its good moduli space is the well-known Hilbert scheme of l points Hilb^l(X). In this talk, I will define a certain enlargement U of this stack and prove that it admits a good moduli space. Furthermore, I will describe a different open substack of U that admits a good moduli space and explain how it yields a surgery diagram via non-GIT wall-crossing. As an application in the toy case l=1, I will explain how this construction helps contract rational curves on higher-dimensional varieties and, time permitting, use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero.
If you cannot make it, talks after posted on youtube afterwards: https://www.youtube.com/@PCTSeminar
JS PL (he/him) (Aug 07 2026 at 00:40):Reminder about today's online seminar talk starting soon at
JS PL (he/him) (Aug 20 2026 at 03:41):Alyssa Renata (Imperial College London) will give a talk for a second edition of this month's PCT seminar (https://pctseminar.github.io/) on
The zoom link to join the seminar is:
https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1
Title: The Game Spectrum of a Monad?
Abstract: In recent work joint with Richard Garner and my supervisor Nicolas Wu, inspired by the computational effects interpretation of monads and algebraic theories due to Moggi, Plotkin and Power, we constructed an adjunction between the category of monads on set and the category of small categories and retrofunctors/cofunctors. Under the computational effects interpretation, the monad encodes computations which may interact with or affect some environment. The left adjoint to this construction assigns to each monad what is called its behaviour category, which may be seen as a model of the environment itself: the objects are the possible states, and the morphisms transitions between states. This adjunction ought to be seen as a kind of duality, with the behaviour category acting as the spectrum of a monad. The first half of the talk will be dedicated to reviewing this construction and its surrounding adjunction.
The second half of the talk is about my recent attempt with Richard at rectifying a defect of the theory: many monads have trivial behaviour category! This is undesirable because of an analogy we want to develop with schemes: the monads replace the (commutative) rings, while the behaviour category should replace the affine schemes. But of course, an affine scheme/spectrum should faithfully encode its corresponding ring/monad, and this is evidently not so for the behaviour category. Our proposal then is to replace the behaviour category by a particular 2-player game (between the program and the environment), from which the data of the behaviour category can be extracted by inspecting its (winning) strategies. The point is that the behaviour category is trivial when there are no winning strategies, but this need not imply triviality of the game itself. To be more precise, we will investigate the relationship with the template games of Paul-Andre Mellies, which he used to build higher-dimensional models of linear logic.
We hope to see you there!
Talks posted on youtube afterwards: https://www.youtube.com/@PCTSeminar
JS PL (he/him) (Aug 20 2026 at 03:41):