Drinfeld centers for bicategories

Abstract

We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral se- quence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automor- phism group of its identity object. There is an associated obstruction theory that explains the difference between the Drinfeld center and the center of the classifying category. For examples, we discuss bicat- egories of groups and bands, rings and bimodules, as well as fusion categories.