Model categories from resolution dimensions

Abstract

We discuss model category structures on abelian categories arising from resolution dimensions. In particular, suppose the subcategory of projective objects is an injective cogenerator of X \mathcal {X} , where X \mathcal {X} is a resolving subcategory contained in the subcategory of Gorenstein projective objects. We can conclude that X \mathcal {X} is Frobenius and the stable category is given by the homotopy category of a corresponding model structure.