Center construction for group-crossed tensor categories

Abstract

We define the notion of the $(G,\Gamma )$-crossed center of a $(G,\Gamma )$-crossed tensor category in the sense of Natale. We show that the $(G,\Gamma )$-crossed center is a $(G\bowtie \Gamma ,G\times \Gamma )$-braided tensor category. This construction generalizes the graded center construction for graded tensor categories and the equivariant center construction for tensor categories with group actions.

19 pages, 9 TikZ figures. Some minor mistakes were fixed in version 2