{"paper":{"title":"Silting reduction and Calabi--Yau reduction of triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dong Yang, Osamu Iyama","submitted_at":"2014-08-12T09:44:12Z","abstract_excerpt":"It is shown that the silting reduction $\\ct/\\thick\\cp$ of a triangulated category $\\ct$ with respect to a presilting subcategory $\\cp$ can be realized as a certain subfactor category of $\\ct$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\\ct$ containing $\\cp$ and the set of (pre)silting subcategories of $\\ct/\\thick\\cp$. This is analogous to a result for Calabi-Yau reduction. This result is applied to show that Amiot-Guo-Keller's construction of $d$-Calabi-Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2678","kind":"arxiv","version":5},"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"}