Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 707-735 |
| Number of pages | 30 |
| Journal | Documenta Mathematica |
| Volume | 20 |
| Publication status | Published - 2015 |
Bibliographical note
Both authors were supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).Keywords
- Drinfeld centers
- bicategories
- spectral sequences
- obstruction theory
- bands
- bimodules
- fusion categories