{"paper":{"title":"Polygon of recollements and $N$-complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Jun-ichi Miyachi, Kiriko Kato, Osamu Iyama","submitted_at":"2016-03-19T07:15:42Z","abstract_excerpt":"We study a structure of subcategories which are called a polygon of recollements in a triangulated category. First, we study a $2n$-gon of recollements in an $(m/n)$-Calabi-Yau triangulated category. Second, we show the homotopy category $\\mathsf{K}(\\mathsf{Mor}_{N-1}(\\mathcal{B}))$ of complexes of an additive category $\\mathsf{Mor}_{N-1}(\\mathcal{B})$ of $N-1$ sequences of split monomorphisms of an additive category $\\mathcal{B}$ has a $2N$-gon of recollments. Third, we show the homotopy category $\\mathsf{K}_{N}(\\mathcal{B})$ of $N$-complexes of $\\mathcal{B}$ has also a $2N$-gon of recollment"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06056","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"}