Module categories over graded fusion categories

TL;DR

This paper classifies module categories over graded fusion categories, especially Tambara Yamagami categories, by relating them to module categories over the base category and extension data, advancing understanding of their structure.

Contribution

It provides a classification framework for module categories over graded fusion categories using extension data, including new results for Tambara Yamagami categories.

Findings

Classified module categories over graded fusion categories.

Described functor categories and dual categories.

Applied classification to Tambara Yamagami categories.

Abstract

Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,a) of C. We also describe functor categories over C (and in particular the dual categories of C). We use this in order to classify module categories over the Tambara Yamagami fusion categories, and their duals.