The Edinburgh category theory seminar runs on most termtime Wednesdays from 12:05 to 13:00, in the Bayes Centre, Room 5.46. Talks are also livestreamed.
The seminar is intended to be an informal environment where people interested in category theory can share ideas. Many of our speakers are internal, with some guests. Talks span a wide range of topics, from higher categories to theoretical computer science, so they should be accessible to anyone with some category theory basics. There is no requirement to talk about cutting-edge research, and, in particular, PhD students should feel comfortable giving an introductory talk on some standard categorical topic.
For more details, or to propose a talk, please email Maia or Tom. There is step-free level access throughout the Bayes Centre, and all toilets are gender-neutral; more information about accessibility of the Bayes Centre is available via AccessAble. Please let one or both of us know if you have any unaccommodated accessibility requirements.
This is one of several seminars run within the Hodge Institute at Edinburgh. The Edinburgh category theory seminar was run by Adrián Doña Mateo and Tom from 2024 to 2026, and by Emily Roff and Ruben Van Belle from 2020 to 2023.
While many category theorists draw inspirations from ideas outside mathematics, I will focus on projects, institutions and software that aim to use category theory to tackle problems that nonmathematicians want solved. My main examples will be those I am most familiar with: the Topos Institute and Topos UK, the category-based software they create (Catlab and Catcolab), the ARIA project on safeguarded AI, which hired many UK category theorists, the new ARIA project on accelerated adaptation for resilience to climate change, and Nathaniel Osgood's project to develop software for epidemiological modeling. I will reflect on some of the difficulties of using category theory for the public good.
Title and abstract TBA
Title and abstract TBA
Title and abstract TBA
Understanding expressions such as "the free monoidal category on a monoid" or "the free finite limit category containing a graph" takes a little work but, once done, opens a surprising number of doors. Walking through these doors, we meet structures as diverse as cobordisms, classifying toposes and Thompson's notorious group F. I will give a round-up.
I plan to give a gentle introduction to the use of triangulated categories in representation theory, including derived categories, stable categories, and singularity categories. I probably won't give all the details of the definition of a triangulated category, but rather concentrate on a few of the axioms, where they come from and how to use them. I might get around to explaining how stable infinity categories are similar but better, and just what extra information they contain.
A pre-monoidal structure on a category C is the data of, for every collection {x_i} of objects in C, a set ⊗{x_i} of "potential" tensor products, satisfying some natural axioms. This is a weakening of the notion of symmetric monoidal category, where such sets always contain exactly one point (the actual tensor product).
A motivating example is the following: given an object x of a symmetric monoidal category C, one cannot expect the slice category C/x to be symmetric monoidal. However, if the unit of C is initial, there is always a natural pre-monoidal structure on C/x. This was originally observed by Karlsson-Scheimbauer-Walde in their study of constructible factorisation algebras, where they used pre-monoidal structures to prove that constructible factorisation algebras can be defined on a multiplicative disk basis.
I will give a formal definition of pre-monoidality via a class of ∞-operads called pre-monoidal. I will then describe a proof that the natural left adjoint from the category of ∞-operads to the category of symmetric monoidal ∞-categories factors through the category of pre-monoidal ∞-operads. Everything is joint with Francesca Pratali.
Metric spaces admit lots of different notions of homomorphism. Well-known examples include continuous, uniformly continuous, Lipschitz, bounded, and distance non-increasing maps. However, the categories of metric spaces with these maps tend to be quite badly behaved: important functors out of them often fail to be continuous. For some notions of homomorphism, there are classical extensions of the naive categories that are better behaved. For example, the category of topological spaces extends the category of metric spaces and continuous maps. In this talk I will present a general procedure for 'correcting' the naive categories by formally adding certain limits and provide an overview of the resulting theory.
Every algebraic theory has some free algebras, and it's tempting to think about these as the algebras that satisfy no equational laws not already present in the theory. But, counterintuitively, this isn't true: e.g. the free group on a single generator, Z, is Abelian, i.e. it satisfies the nontrivial equational law xy = yx. (Furthermore, not all algebras that satisfy no equational laws are free: consider e.g. an infinite power of Z in the theory of Abelian groups.) Tom Leinster and I have been looking into what's going on here, and I'll spend this talk talking about my current, very much unfinished thoughts.
This sentence was last updated on 2026-11-04.