{"paper":{"title":"Subfactor categories of triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Baiyu Ouyang, Jinde Xu, Panyue Zhou","submitted_at":"2014-04-19T07:09:05Z","abstract_excerpt":"Let {\\cal T} be a triangulated category, {\\cal A} a full subcategory of {\\cal T} and {\\cal X} a functorially finite subcategory of {\\cal A}. If {\\cal A} has the properties that any {\\cal X}-monomorphism of {\\cal A} has a cone and any {\\cal X}-epimorphism has a cocone. Then the subfactor category {\\cal A/[X]} admits a pretriangulated structure in the sense of [BR]. Moreover the above pretriangulated category {\\cal A/[X]} with ({\\cal X},{\\cal X}[1]) = 0 becomes a triangulated category if and only if ({\\cal A},{\\cal A}) forms an {\\cal X}-mutation pair and {\\cal A} is closed under extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4930","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"}