Equivariant categories from categorical group actions on monoidal categories

TL;DR

This paper generalizes the construction of G-equivariant categories from Hopf algebra actions to weak group actions on arbitrary monoidal categories, expanding the framework for 3d homotopy field theories.

Contribution

It introduces a method to construct G-equivariant categories from weak group actions on monoidal categories, broadening the scope beyond Hopf algebra automorphisms.

Findings

Constructed G-equivariant categories with neutral component as the Drinfeld center of C.

Extended the framework to weak (not strict) group actions.

Provided a generalized approach applicable to arbitrary monoidal categories.

Abstract

G-equivariant modular categories provide the input for a standard method to construct 3d homotopy field theories. Virelizier constructed a G-equivariant category from the action of a group G on a Hopf algebra H by Hopf algebra automorphisms. The neutral component of his category is the Drinfeld center of the category of H-modules. We generalize this construction to weak actions of a group G on an arbitrary monoidal category C by (possibly non-strict) monoidal auto-equivalences and obtain a G-equivariant category with neutral component the Drinfeld center of C.