Stability of Gorenstein Categories

Abstract

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 $G=...\xra{\partial^G_2}G_1\xra{\partial^G_1}G_0\xra{\partial^G_0} ...$ such that the complexes $\Hom_R(G,H)$ and $\Hom_R(H,G)$ are exact for each Gorenstein projective $R$-module $H$, the module $\coker(\partial^G_1)$ is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.

21 pages, uses XY-pic. Version 2 contains corrected proofs of Lemma 2.1 and Theorem 4.8

Cited by in corpus (6)

• Frobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts
• Homological Dimensions Relative to Preresolving Subcategories
• Relative Singularity Categories
• Stability of strongly Gorenstein flat modules
• Finiteness criteria for Gorenstein flat dimension and stability
• Duality Pairs Induced by One-Sided Gorenstein Subcategories