  In this paper we consider categories over a commutative ring provided either
with a free action or with a grading of a not necessarily finite group. We
define the smash product category and the skew category and we show that these
constructions agree with the usual ones for algebras. In case of the smash
product for an infinite group our construction specialized for a ring agrees
with M. Beattie's construction of a ring with local units in \cite{be}. We
recover in a categorical generalized setting the Duality Theorems of M. Cohen
and S. Montgomery in \cite{cm}, and we provide a unification with the results
on coverings of quivers and relations by E. Green in \cite{g}. We obtain a
confirmation in a quiver and relations free categorical setting that both
constructions are mutual inverses, namely the quotient of a free action
category and the smash product of a graded category. Finally we describe
functorial relations between the representation theories of a category and of a
Galois cover of it.
