Which 2-Segal spaces induce Multi-fusion categories?MPIM

by Jonte Gödicke (MPIM)

Tuesday Jan 13, 2026, 11:00 AM → 12:30 PM Europe/Berlin

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

Abstract Homotopy Theory Seminar

In the theory of 3-dimensional Topological Field Theories (short TFTs), certain monoidal categories called multi-fusion categories are of fundamental importance. Well-known simple examples of these arise from finite groups via a linearization construction. However,  from the same construction also more interesting examples of monoidal categories can be constructed from any 2-Segal space. These include so-called Hall monoidal categories, which are anticipated to have interesting connections to certain TFTs.

In this talk, I will discuss the question, which 2-Segal spaces induce multi-fusion categories. For this, I will introduce a 2-categorical characterization of multi-fusion categories to translate questions about these monoidal structures to questions about homotopy coherent algebra in (∞,2)-categories of spans.