nLab module category

This page is about actions of tensor categories. For categories of modules or actions of monoidal categories, see there.

Idea

A module category is a linear category equipped with an action of a tensor linear category. That is, a module category is an actegory enriched in $K\mathbf{Mod}$, or a pseudoaction internal to $K\mathbf{Mod}$-$\mathbf{Cat}$.

Related concepts

• actegory

• 2-module, n-module

• bimodule category

• module

• module 2-category

• module over a monoidal functor

References

• Victor Ostrik: Module categories, weak Hopf algebras and modular invariants, Transformation Groups 8 (2003) 177-206 [doi:10.1007/s00031-003-0515-6, arXiv:0111139]

• Chris Douglas, Chris Schommer-Pries, Noah Snyder: Dualizable tensor categories [arXiv:1312.7188]