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‐modules G=⋯→∂2GG1→∂1GG0→∂0G⋯ such that the complexes HomR(G, H) and HomR(H, G) are exact for each Gorenstein projective R‐module H, the module Coker (∂1G) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.