Braided Picard groups and graded extensions of braided tensor categories

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