Drinfeld Centers for Bicategories

We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral sequence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automorphism 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 bicategories of groups and bands, rings and bimodules, as well as fusion categories.

2010 Mathematics Subject Classification: Primary 18D05; Secondary 55T99.

Keywords and Phrases: Drinfeld centers, bicategories, spectral sequences, obstruction theory, bands, bimodules, fusion categories.

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