Category-valued traces for bimodule categories: a representation-theoretic realization

Abstract

The category-valued trace assigns to a bimodule category over a linear monoidal category a linear category. It generalizes Drinfeld centers of monoidal categories and the relative Deligne product of bimodule categories. In this article, we study bimodule categories that are given as categories of bicomodules over a Hopf algebra. Our main result is a representation-theoretic realization of the category-valued trace as a category of generalized Hopf bimodules.

Keywords:

• Bimodule categories over monoidal categories
• Hopf algebras
• Drinfeld center
• Hopf bimodules

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W30
• 18D10
• 18D05

Acknowledgments

The author is very grateful to Christoph Schweigert for supervising this project and for providing constant encouragement and advice. The author would also like to thank Ehud Meir for helpful comments on a draft version of this paper. The author is supported by the RTG 1670 “Mathematics inspired by String theory and Quantum Field Theory”.

Disclosure statement

No potential conflict of interest was reported by the author.