  For an adjoint pair $(F, G)$ of functors, we prove that $G$ is a separable
functor if and only if the defined monad is separable and the associated
comparison functor is an equivalence up to retracts. In this case, under an
idempotent completeness condition, the adjoint pair $(F, G)$ is monadic. This
applies to the comparison between the derived category of the category of
equivariant objects in an abelian category and the category of equivariant
objects in the derived category of the abelian category.
