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arXiv · 1711.00645

Equivalences of Graded Categories

Cain Edie-Michell
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Abstract

We further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the $\mathcal{C}$-based equivalences between two $G$-graded extensions of $\mathcal{C}$. The main result of this paper (which follows from this classification) shows that there is an action of the group $\operatorname{Aut}(G)\times \operatorname{Aut}_\otimes(\mathcal{C})$ on the set of all $G$-graded extensions of $\mathcal{C}$, and further, any two extensions in the same orbit of this action are monoidally equivalent. As a warm up for the proof of our classification result we reprove the classification of graded extensions of a fusion category, making extensive use of graphical calculus. Aside from our main result, we provide several other practical applications of our classification of $\mathcal{C}$-based equivalences.

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Cain Edie-Michell. 2017-11-02. Equivalences of Graded Categories. https://arxiv.org/abs/1711.00645

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