The study and classification of algebra objects in modular tensor categories has a strong motivation from the conformal field theoretical point of view, these objects being related to e.g. full theories [Fuchs-Runkel-Schweigert] and extensions of vertex operator algebras [Huang-Kirillov-Lepowsky, Creutzig-Kanade-McRae for superalgebras]. In this talk, I will present a classification of rigid, Frobenius algebras in the so-called Dijkgraaf-Witten categories, which we achieved using Frobenius monoidal functors. Joint work with Robert Laugwitz and Sam Hannah, based on SIGMA 19 (2023), 075, 42 pages.
