{"paper":{"title":"Stability of Gorenstein Categories","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Diana White, Sean Sather-Wagstaff, Tirdad Sharif","submitted_at":"2007-03-21T19:44:02Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703644","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}