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

Equivariant categories from categorical group actions on monoidal categories