  Recently, Chach\'olski, Neeman, Pitsch, and Scherer studied, in a series of
three papers, model approximations for the unbounded category of cochain
complexes over a commutative ring. These approximations allow to construct
relative injective resolutions with respect to particular choices of
injectives. In this paper we define similar model approximations for cochain
complexes on general Grothendieck categories generalizing the previous
constructions and reaching a better understanding of the whole picture.
