PRESERVING AND REFLECTING COVERS BY FUNCTORS - APPLICATIONS TO GRADEDMODULES

We study G-covers in the context of Grothendieck categories. Namely, w e analyse when a functor between two Grothendieck categories preserves or reflects G-covers. We apply our general study to the category of g raded modules over a graded ring, by showing that relative injective c overs with respect to a torsion theory are preserved and reflected, in some cases,among the categories R-gr, R(1)-Mod and R-Mod.