{"paper":{"title":"The Extension Dimension of Abelian Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Junling Zheng, Xin Ma, Zhaoyong Huang","submitted_at":"2019-02-25T10:15:37Z","abstract_excerpt":"Let $\\A$ be an abelian category having enough projective objects and enough injective objects. We prove that if $\\A$ admits an additive generating object, then the extension dimension and the weak resolution dimension of $\\A$ are identical, and they are at most the representation dimension of $\\A$ minus two. By using it, for a right Morita ring $\\La$, we establish the relation between the extension dimension of the category $\\mod \\La$ of finitely generated right $\\Lambda$-modules and the representation dimension as well as the right global dimension of $\\Lambda$. In particular, we give an uppe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09176","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"}