Pacific Category Theory Seminar
The Pacific Category Theory (PCT) seminar is an online seminar for the category theory community in the Asia-Pacific time zone and beyond. We aim to cover topics in all areas of pure and applied category theory in relationship with other disciplines.
The seminar will run once a month on Friday at 10am JST/11am AED (1am UTC). Here is the zoom link to partipate. Previous talks are available on the seminar's youtube channel.
Upcoming talks
May 8, 2026
- Speaker: Ross Street (Macquarie University)
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.
June 5, 2026
- Speaker: Thomas Seiller (CNRS, JFLI)
Previous talks
April 24, 2026
- Speaker: Dusko Pavlovic (University of Hawaii)
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.
Recording and slides
March 27, 2026
- Speaker: Rose Kudzman-Blais (RIMS, Kyoto University)
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.
Recording and slides
February 27, 2026
- Speaker: Yuki Imamura (RIMS, Kyoto University)
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.
Recording and slides
January 16, 2026
- Speaker: Taichi Uemura (Nagoya University)
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.
Recording and slides
December 12, 2025
- Speaker: Richard Garner (Macquarie University)
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!
Recording and slides