We classify various types of graded extensions of a finite braided tensor category \(\mathcal {B}\) in terms of its 2-categorical Picard groups. In particular, we prove that braided extensions of \(\mathcal {B}\) by a finite group A correspond to braided monoidal 2-functors from A to the braided 2-categorical Picard group of \(\mathcal {B}\) (consisting of invertible central \(\mathcal {B}\)-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.

我们根据其 2-categorical Picard 群对有限编织张量类别\(\mathcal {B}\) 的各种类型的分级扩展进行分类。特别地，我们证明了有限群A对\(\mathcal {B}\)的编织扩展对应于从A到\(\mathcal {B}\)的编织 2-categorical Picard 群的编织幺半群2-函子（由可逆中心\(\mathcal {B}\) -模块类别组成）。这样的函子可以用 Eilnberg-Mac Lane 上同调表示。我们详细描述了对称融合类别和尖头编织融合类别的编织 2 分类 Picard 组。