{"paper":{"title":"Gorenstein homological dimensions for extriangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Dongdong Zhang, Jiangsheng Hu, Panyue Zhou","submitted_at":"2019-08-01T14:59:01Z","abstract_excerpt":"Let $(\\mathcal{C},\\mathbb{E},\\mathfrak{s})$ be an extriangulated category with a proper class $\\xi$ of $\\mathbb{E}$-triangles. The authors introduced and studied $\\xi$-$\\mathcal{G}$projective and $\\xi$-$\\mathcal{G}$injective in \\cite{HZZ}. In this paper, we discuss Gorenstein homological dimensions for extriangulated categories. More precisely, we first give some characterizations of $\\xi$-$\\mathcal{G}$projective dimension by using derived functors on $\\mathcal{C}$. Second, let $\\mathcal{P}(\\xi)$ (resp. $\\mathcal{I}(\\xi)$) be a generating (resp. cogenerating) subcategory of $\\mathcal{C}$. We s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00931","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00931/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}