Stability of Gorenstein categories

We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective R ‐modulesG = ⋯ → ∂ 2 GG 1 → ∂ 1 GG 0 → ∂ 0 G⋯such that the complexes Hom R ( G, H ) and Hom R ( H, G ) are exact for each Gorenstein projective R ‐module H , the module Coker ( ∂ 1 G ) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.