Rigid monoidal 2-categories from non-semisimple braided tensor categories

by Robert Laugwitz (Nottingham)

Thursday 15 Jan 2026, 16:15 → 17:15 Europe/Berlin

H3 (Geomatikum)

Fusion categories, and more generally tensor categories, have a wealth of applications in topology and mathematical physics. Recently, a theory of fusion 2‑categories, generalizing that of fusion categories to monoidal 2‑categories, has been developed. It is established that fusion 2‑categories have strong rigidity properties: all objects have duals and all 1‑morphisms have adjoints. Semisimple module categories over a braided fusion category provide a broad class of examples of fusion 2‑categories.
 
In this talk, I will report on a new class of perfect module categories, a subclass of exact module categories over a braided tensor category. These give monoidal 2‑categories that retain the same rigidity properties as fusion 2‑categories but are locally non‑semisimple. This is joint work in progress with Azat Gainutdinov (Tours).