Wintersemester 2025/26

Wintersemester 2025/26

12.11.2025 um 15:00 Uhr in 69/127

Dr. Paula Verdugo (MPIM Bonn)

On the equivalence invariance of formal category theory

Equipments, a special kind of double categories, have shown to be a powerful environment to express formal category theory. We build a model structure on the category of double categories and double functors whose fibrant objects are the equipments, and combine this together with Makkai’s early approach to equivalence invariant statements in higher category theory via FOLDS (First Order Logic with Dependent Sorts) and Henry’s recent connection between model structures and formal languages, to show a result on the equivalence invariance of formal category theory.

15.12.2025 um 14:00 Uhr in 66/E01

Dr. Georg Lehner (Universität Münster)

On Verdier Duality

Recent progress on the K-theory of "large" categories has raised interest in the algebraic K-theory of sheaves on locally compact Hausdorff spaces, which serves as a central stepping stone to modern approaches to assembly conjectures in K-theory and L-theory. A central ingredient for the computation of the K-theory of these sheaf categories is Verdier duality: The categories of sheaves and cosheaves agree when the target is a stable category.

We present a category-theoretic perspective on this computation by analyzing the notion of a continuous algebra of a lax-idempotent monad. As a result we obtain a completely formal generalization of Verdier duality to a larger class of spaces - so-called stably locally compact spaces. We will elaborate on the role of classical Stone duality, as well as sketch a proof of the computation of the algebraic K-theory of a coherent space.