Kenichi Shimizu
Shibaura Institute of Technology, Saitama, Japan

This talk is based on my joint work with Taiki Shibata. A Hopf algebra is said to be co-Frobenius if it admits a non-zero cointegral. A Frobenius tensor category is an abstraction of the category of comodules over a co-Frobenius Hopf algebra. In this talk, I will present recent results on Frobenius tensor categories generalizing known results on co-Frobenius Hopf algebra. A technical difficulty compared to the case of Hopf algebras is that there is no obvious notion of cointegrals for tensor categories. Our opinion is that the Nakayama functor for a locally finite abelian category alternates cointegrals in a categorical setting. I will introduce basic results on the Nakayama functor and outline the proof of our recent result that the class of Frobenius tensor categories is closed under exact sequences.