{"paper":{"title":"Derived categories of $N$-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":"2013-09-24T03:46:23Z","abstract_excerpt":"We study the homotopy category $\\mathsf{K}_{N}(\\mathcal{B})$ of $N$-complexes of an additive category $\\mathcal{B}$ and the derived category $\\mathsf{D}_{N}(\\mathcal{A})$ of an abelian category $\\mathcal{A}$. First we show that both $\\mathsf{K}_N(\\mathcal{B})$ and $\\mathsf{D}_N(\\mathcal{A})$ have natural structures of triangulated categories. Then we establish a theory of projective (resp., injective) resolutions and derived functors. Finally, under some conditions of an abelian category $\\mathcal{A}$, we show that $\\mathsf{D}_{N}(\\mathcal{A})$ is triangle equivalent to the ordinary derived ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6039","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"}