Frobenius properties of tensor functors

This note is an announcement of my recent work on Frobenius properties of tensor functors between finite tensor categories. Fischman, Montgomery and Schneider showed that the Frobenius property of an extension A/B of finite-dimensional Hopf algebras is controlled by the modular functions of A and B. In this note, I explain how their result can be extended in the framework of finite tensor categories, a class of tensor categories including the representation category of a finite-dimensional Hopf algebra. I also introduce the “braided version” of their theorem