### 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 multiplicatively 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 $G$.

Publication

J. Lond. Math. Soc. (2) 83 (2011), no. 1, 57–78.