David Jaklitsch: ⊗-Frobenius functors and exact module categories

Abstract: Frobenius algebras are structures relevant in multiple disciplines such as subfactor theory, conformal field theory or topological field theory. The purpose of the talk is to present some recent results based on arxiv:2501.16978 about preservation and construction of Frobenius algebras. To this end, we recall the notions of Frobenius and Frobenius monoidal functors. We introduce the notion of ⊗-Frobenius functors and provide characterizations relating them with the other Frobenius-type functors. These are used to twist module categories. Results on necessary and sufficient conditions for the preservation of certain properties under twisting and preservation of Frobenius algebras are summarized.