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Meeting 41 - Manchester

Meeting #41 of YaMCATS will happen:

9th June 2026 (University of Manchester)

Schedule

  • 13:00 -- 14:00: David Jordan
  • 14:00 -- 14:30: Coffee break
  • 14:30 -- 15:30: Vít Jelínek
  • 15:30 -- 16:00 Coffee break
  • 16:00 -- 17:00 Joanna Ko.
  • 17:00 -- onwards: Informal Discussions / Pub / Dinner.

If you wish to attend this meeting, please register by using this link by 12:00noon (UK time) on Thursday 4th June 2026. This will facilitate us organising the coffee breaks and dinner, and preparing the final report of the network, as required by LMS.

Venue: Alan Turing Building, University of Manchester. Frank Adams room (level 1).

Oxford Road train station is ~10 minutes walk, Piccadilly train station is ~25 minutes walk. Manchester Victoria train station ~40 minutes walk.

Titles and abstracts:

  • David Jordan (University of Edinburgh)
    • Title: Finiteness for skein categories.
    • Abstract: Skein categories are diagrammatically defined categories important in quantum topology (the field which studies topology of 2-, 3- and 4-manifolds via tensor categories and related topics).  In this talk I'll outline what skein categories are, and how to apply some tools from category theory.  I'll explain a "finiteness" conjecture of Sam Gunningham, Monica Vazirani and myself asserting that their Yoneda categories have a compact projective generator, and I'll outline a proof we have developed with Renaud Detcherry.
  • Vít Jelínek (University of Sussex)
    • Title: Pseudomonadicity of Dependent Type Theories.
    • Abstract: Historically, semantics of dependent type theory (DTT) had been studied on a case by case basis: one could study the semantics of DTT with $\Sigma$-types and then one could also independently study the semantics of DTT with $\Pi$-types. A more uniform approach first required a definition of a DTT. One proposal for such a definition was given by Taichi Uemura: in the spirit of functorial semantics, a DTT is a small category with finite limits and a class of exponentiable arrows. Models of such a theory $T$ are functors out of $T$ preserving all the structure. In this talk, we will study the 2-category of dependent type theories and explain why it is pseudomonadic over a 2-category of categories equipped with a class of arrows and a class of commutative squares.This is a joint work with John Bourke.
  • Joanna Ko (Topos Institute, Oxford)
    • Title: Models of Enhanced 2-sketches & Algebras over Enhanced 2-monads.
    • Abstract: We study the enhanced 2-category of models of enhanced limit 2-sketches with tight weighted cones. We show that for any enhanced limit 2-sketch $\mathbb{T}$ with tight cones, the enhanced 2-category $\mathbb{M}\mathrm{od}_{s, w}(\mathbb{T}, \mathbb{K})$ of models of $\mathbb{T}$ in a locally presentable enhanced 2-category $\mathbb{K}$, in which the tight and the loose morphisms are the $\mathscr{F}$-natural transformations and the loose $w$-natural transformations, respectively, is equivalent to the enhanced 2-category ${\mathrm{T}\text{-}\mathbb{A}\mathrm{lg}}_{s, w}$ of algebras over an enhanced 2-monad $T$ on the models $\mathbb{M}\mathrm{od}(\mathcal{T}_\tau, \mathbb{K})$ restricted to the tight morphisms in $\mathbb{T}$ with strict $T$-morphisms and $w$-$T$-morphisms.Along the way, we establish an enriched analogue of the Orthogonal Sub-category Theorem, and generalise results on the reflectivity and the monadicity of models of enriched limit sketches in the base of enrichment to any arbitrary locally presentable enriched category.