{"paper":{"title":"$n$-abelian quotient categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Zhu, Panyue Zhou","submitted_at":"2018-07-18T01:19:19Z","abstract_excerpt":"Let $\\C$ be an $(n+2)$-angulated category with shift functor $\\Sigma$ and $\\X$ be a cluster-tilting subcategory of $\\C$. Then we show that the quotient category $\\C/\\X$ is an $n$-abelian category. If $\\C$ has a Serre functor, then $\\C/\\X$ is equivalent to an $n$-cluster tilting subcategory of an abelian category $\\textrm{mod}(\\Sigma^{-1}\\X)$. Moreover, we also prove that $\\textrm{mod}(\\Sigma^{-1}\\X)$ is Gorenstein of Gorenstein dimension at most $n$. As an application, we generalize recent results of Jacobsen-J{\\o}rgensen and Koenig-Zhu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06733","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"}