{"paper":{"title":"The homotopy category of flat functors","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ali Zaghian, Esmaeil Hosseini","submitted_at":"2017-05-14T08:55:35Z","abstract_excerpt":"Let C be a small category and G be a tensor Grothendieck category. We define a notion of atness in the category Fun(C; G) of all covariant functors from C to G and show that the inclusion K(FlatA) ---> K(A) has a right adjoint where K(A) is the homotopy category of A and K(FlatA) its subcategory consisting of complexes of at functors. In addition, we find a replacement for the quotient Dpac(FlatA) = K(FlatA)Kp(FlatA) of triangulated categories where Kp(FlatA) is the homotopy category of all pure acyclic complexes of at functors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04930","kind":"arxiv","version":3},"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"}