Moscow Mathematical Journal

Volume 17, Issue 1, January–March 2017 pp. 97–128.

Module Categories over Equivariantized Tensor Categories

Authors: Martín Mombelli (1) and Sonia Natale (1)
Author institution:(1) Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM – CONICET, Medina Allende s/n, (5000) Ciudad Universitaria, Córdoba, Argentina

Summary:

For a finite tensor category 𝒞 and a Hopf monad T: 𝒞→𝒞 satisfying certain conditions we describe exact indecomposable left 𝒞^T-module categories in terms of left 𝒞-module categories and some extra data. We also give a 2-categorical interpretation of the process of equivariantization of module categories.

2010 Math. Subj. Class. 18D10, 16T05.

Keywords: Tensor category, module category, Hopf monad.

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