Tensor functors between Morita duals of fusion categories.


Given a fusion category $\mathcal{C}$ and an indecomposable $\mathcal{C}$-module category $\mathcal{M}$, the fusion category $\mathcal{C}_{\mathcal{M}}^{*}$ of $\mathcal{C}$-module endofunctors of $\mathcal{M}$ is called the (Morita) dual fusion category of $\mathcal{C}$ with respect to $\mathcal{M}$. We describe tensor functors between two arbitrary duals $\mathcal{C}_{\mathcal{M}}^{*}$ and $\mathcal{D}_{\mathcal{N}}^{*}$ in terms of data associated to $\mathcal{C}$ and $\mathcal{D}$. We apply the results to $G$-equivariantizations of fusion categories and group-theoretical fusion categories. We describe the orbits of the action of the Brauer-Picard group on the set of module categories and we propose a categorification of the Rosenberg-Zelinsky sequence for fusion categories.

Lett. Math. Phys. 107 (2017), no. 3, 553–590
César Galindo
Associate Professor of Mathematics

My research interests include representation theory, category theory and their applications to Mathematical-Physics.