Mateusz StroinskiMPIM

by Mateusz Stroinski (Universität Hamburg)

Tuesday Nov 17, 2026, 11:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract Homotopy Theory Seminar

Finite tensor (1-)categories are monoidal categories which generalize categories of modules over finite-dimensional Hopf algebras, e.g. group algebras. Beyond representation theory, they are useful in the construction of 3-dimensional topological field theories. Towards 4D TFTs, Douglas and Reutter introduced fusion 2-categories, which are the "semisimple categorification" of finite tensor categories. In this talk, I will introduce a non-semisimple generalization and some early results about them. In concrete terms, the main result on which we build our theory is a characterization of 2-categories of module categories over tensor (1-)categories - this relies on combining some representation theory of finite-dimensional algebras with the results of Street and Garner--Shulman which characterize enriched profunctors as a free cocompletion.