Clifford theory for tensor categories

Abstract

A graded tensor category over a group $G$ will be called a strongly $G$-graded tensor category if every homogeneous component has at least one multiplicativily invertible object. Our main result is a description of the module categories over a strongly $G$-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of $G$.

Final version.

Cited by in corpus (4)

• Fermionic Modular Categories and the 16-fold Way
• On Gauging Symmetry of Modular Categories
• Eilenberg-Watts Theorem for 2-categories and quasi-monoidal structures for module categories over bialgebroid categories
• Compact Semisimple Tensor 2-Categories are Morita Connected