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Meeting 39 (Leeds)

Wednesday, 21st January 2026. University of Leeds.

Hosted by the University of Leeds. Supported by the London Mathematical Society.
The meeting will be held in the School of Mathematics at the University of Leeds. A link to the campus map is here.

This event is free and open to everyone.

Speakers

Schedule

  • 13:00 - 14:00: Mark Kamsma, Cofibrant generation of pure monomorphisms in presheaf categories.
  • 14:00 - 14:30: Coffee break
  • 14:30 - 15:30: Chris Heunen, Control, Complete, Compute: Rig Categories in Quantum Computing.
  • 15:30 - 16:00: Coffee break
  • 16:00 - 17:00: Robert Laugwitz, Induced functors between Drinfeld centers of tensor categories.
  • 17:00 - onwards: Informal discussions / pub / dinner.

All talks will be held in MALL (Level 8 of the School of Maths).
Coffee breaks at MRD (Maths Research Deck); follow the signs.

Titles and Abstracts:

  • Mark Kamsma (Masaryk University, Brno)
    • Title: Cofibrant generation of pure monomorphisms in presheaf categories
    • Abstract: For a fixed monoid $S$, there is an algebraic question whether or not pure monomorphisms between sets with an $S$-action are cofibrantly generated. Pure monomorphisms are precisely those monomorphisms that reflect solutions to systems of equations. Viewing presheaves as multi-sorted unary algebras, we can extend the question to: when are the pure monomorphisms in a presheaf category cofibrantly generated? We give a simple characterisation of when this happens. For sets with an $S$-action this is exactly when for all $a, b \in S$ there is $c \in S$ with $a = cb$ or $b = ca$. Our proof is model-theoretic and uses the recently developed categorical approach to stability theory.This is joint work with Sean Cox, Jonathan Feigert, Marcos Mazari-Armida and Jiří Rosický..
  • Chris Heunen (University of Edinburgh)
    • Title: Control, Complete, Compute: Rig Categories in Quantum Computing.
    • Abstract: We present a categorical axiomatisation of quantum computation based on free constructions. Starting from a PROP of base circuits, we introduce a theory of computational control given by eight natural equations, and show that adjoining control syntactically corresponds semantically to completing the PROP to its free rig category. Next, we show that two further generators and three further equations suffice to fully characterise quantum computing. The resulting free model replaces the usual linear-algebraic semantics with a purely symbolic, combinatorial one. We argue that this gives a conceptually simpler foundation for quantum computing that isolates quantum advantage in a precise categorical sense. (Based on joint work with Robin Kaarsgaard, Louis Lemonnier, Neil Julien Ross, Amr Sabry, and Jacques Carette.)
  • Robert Laugwitz (University of Nottingham)
    • Title: Induced functors between Drinfeld centers of tensor categories.
    • Abstract: The Drinfeld center (or monoidal center) is a categorical analogue of the center of a monoid (ring, or algebra). Similarly to the classical structures, a monoidal functor does not induce a functor on the Drinfeld centers. However, we show that adjoints of monoidal functors between monoidal categories lift to functors between the respective Drinfeld centers. These functors are either lax or oplax monoidal (depending on whether they are induced by right or left adjoints). Under some additional conditions, the lax and oplax structures define a Frobenius monoidal functor. The general constructions can be demonstrated using examples coming from extensions of Hopf algebras.  This talk is based on joint work with Johannes Flake (Bonn) and Sebastian Posur (Münster).