Centers of braided tensor categories

Let C be a finite braided multitensor category. Then the end B = fX is an element of C X circle times X* is natural a Hopf algebra in C. We show that the Drinfeld center of C is isomorphic to the category of left B- comodules in C, and the decomposition of B into a direct sum of indecomposable C-subcoalgebras leads to a decomposition of B-Comod C into a direct sum of indecomposable C-module subcategories.As an application, we present an explicit characterization of the structure of irreducible Yetter-Drinfeld modules over semisimple and cosemisimple quasi-triangular weak Hopf algebras. Our results generalize those results on finite groups and on quasi-triangular Hopf algebras.(c) 2022 Elsevier Inc. All rights reserved.