The homotopy category of acyclic complexes of pure-projective modules

Abstract

Abstract Let R be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective R-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put this homotopy category into a recollement with two other compactly generated triangulated categories: The usual derived category of R and the pure derived category of R.