We introduce the notion of a reflection fusion category, which is a type of a $G$-crossed category generated by objects of Frobenius-Perron dimension 1 and $\sqrt{p}$, where $p$ is an odd prime. We show that such categories correspond to orthogonal …

We classify all modular categories of dimension 4m, where m is an odd square-free integer, and all ranks 6 and 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. Our results …

We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category $\mathcal{C}$ graded by a group $G$ as induced from module categories over fusion …

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