{"paper":{"title":"Stability of Gorenstein objects in triangulated categories","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Chunli Liang, Zhanping Wang","submitted_at":"2014-09-25T14:41:04Z","abstract_excerpt":"Let $\\mathcal{C}$ be a triangulated category with a proper class $\\xi$ of triangles. Asadollahi and Salarian introduced and studied $\\xi$-Gorenstein projective and $\\xi$-Gorenstein injective objects, and developed Gorenstein homological algebra in $\\mathcal{C}$. In this paper, we further study Gorenstein homological properties for a triangulated category. First, we discuss the stability of $\\xi$-Gorenstein projective objects, and show that the subcategory $\\mathcal{GP}(\\xi)$ of all $\\xi$-Gorenstein projective objects has a strong stability. That is, an iteration of the procedure used to define"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7274","kind":"arxiv","version":1},"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"}