Resumen de Braided Picard groups and graded extensions of braided tensor categories

Alexei Davydov, Dmitri Nikshych

• We classify various types of graded extensions of a finite braided tensor category B in terms of its 2-categorical Picard groups. In particular, we prove that braided extensions of B by a finite group A correspond to braided monoidal 2-functors from A to the braided 2-categorical Picard group of B (consisting of invertible central B-module categories). Such functors can be expressed in terms of the Eilnberg-Mac Lane cohomology. We describe in detail braided 2-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.