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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): JS PL (he/him) (Aug 28 2026 at 00:35):Reminder about today's online seminar talk starting soon at
JS PL (he/him) (Sep 04 2026 at 00:28):Yuki Maehara (Tokyo Metropolitan 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 a homotopy theory of algebraic weak ω-categories
Abstract:
Mainstream models of weak infinite-dimensional categories (such as
quasi-categories or complicial sets) are based on certain non-globular
shapes (such as simplices). This allows one to encode the desired
category-like structure as an existence property. For example,
composition of 1-cells can be encoded as "for any composable pair f
and g, there exists a triangle two of whose edges are f and g", and
such a triangle exhibits the third edge as a composite of f and g. We
don't require this triangle to be unique for given f and g, so
composition is not well defined on the nose. This makes it impossible
even to state strict axioms, and hence the resulting model is
necessarily weak. But it is not too weak — composition is still
"essentially" unique, satisfies the unit and associativity laws "up to
equivalence", and so on — thanks to similar existence properties of
higher-dimensional shapes.
What happens if we instead use the familiar globes so that, for
example, the boundary of a 2-cell is given by a parallel pair of
1-cells rather than a triangle? Well, the 2-globe (or in fact the
n-globe for any n) doesn't contain a composable pair of 1-cells, so
now we must encode composition as an actual algebraic operation rather
than as an existence property; this is what "algebraic" means in the
title of this talk. I will give an overview of a joint project with
Soichiro Fujii and Keisuke Hoshino on such algebraic weak
ω-categories, namely those of Batanin and Leinster, which are the
Eilenberg–Moore algebras for a suitable monad on the category of
globular sets.
Compared with the mainstream models (formulated in the language of
model categories or ∞-categories), this definition has the downside
that it does not naturally come equipped with a homotopy theory, which
makes it difficult to capture up-to-equivalence phenomena and
constructions. On the other hand, it has the upside that these
algebraic weak ω-categories feel much closer to strict ω-categories,
particularly because not only the shapes of the cells but also the
algebraic structure is designed to mirror the familiar behaviour of
their strict counterparts. The overarching theme of this project is
therefore to develop a suitable homotopy theory of algebraic weak
ω-categories, drawing on the strict case for as much intuition — and
even proof strategies — as possible.
We hope to see you there!
Talks are posted on YouTube afterwards:
https://www.youtube.com/@PCTSeminar
JS PL (he/him) (Sep 11 2026 at 00:28):Reminder about today's PCT Seminar starting soon.
JS PL (he/him) (Oct 20 2026 at 09:56):Nadish de Silva (Simon Fraser 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: The Quantum Monad on Relational Structures
Abstract: Homomorphisms between relational structures play a central role
in finite model theory, constraint satisfaction and database theory. A
central theme in quantum computation is to show how quantum resources can
be used to gain advantage in information processing tasks. In particular,
non local games have been used to exhibit quantum advantage in boolean
constraint satisfaction, and to obtain quantum versions of graph
invariants such as the chromatic number. We show how quantum strategies
for homomorphism games between relational structures can be viewed as
Kleisli morphisms for a quantum monad on the (classical) category of
relational structures and homomorphisms. We show a general connection
between these notions and state-independent quantum realizations of strong
contextuality in the Abramsky-Brandenburger formulation of contextuality.
We use these results to exhibit a wide range of examples of
contextuality-powered quantum advantage, and to unify several apparently
diverse strands of previous work.
Co-authors: Samson Abramsky, Rui Soares Barbosa, Octavio Zapata
We hope to see you there!
David Michael Roberts (Oct 21 2026 at 01:14):For reference, I think this is the paper https://arxiv.org/abs/1705.07310
JS PL (he/him) (Oct 23 2026 at 00:35):Reminder about today's PCT Seminar starting soon.
JS PL (he/him) (Nov 06 2026 at 02:25):Geoff Vooys 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: Differential Bundles in the Opposite Category of Schemes
Abstract: A recurring and important theme in tangent category theory (and applications to other areas of mathematics) lies in the use of tangent-categorical techniques to study, understand, and frame concepts which arise in algebraic geometry. For instance, a great deal of work has gone into learning about the tangent category of schemes and its categories of differential bundles; however, comparatively little has been done directly with the opposite category of schemes and the kind of geometry that said opposite category encodes. In this talk we will get to know the opposite category of schemes as a tangent category and see explicitly how to work with this category directly --- a notable theme lies in the interplay between descent-theoretic arguments and tangent-categorical machinery. We will illustrate this by showing that for any scheme X, there is an equivalence of categories between the differential bundles over X (in the opposite category of schemes) and the category of quasi-coherent sheaves on X.
We hope to see you there!
Talks are posted afterwards on youtube: https://www.youtube.com/@PCTSeminar