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/12pm AED (1am UTC). Here is the zoom link to partipate. Previous talks are available on the seminar's youtube channel.
Upcoming talks
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.
April 24, 2026
- Speaker: Dusko Pavlovic (University of Hawaii)
Previous talks
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