{"paper":{"title":"A new Frobenius exact structure on the category of complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Xian-Neng Du, Yan-Fu Ben, Yan-Hong Bao","submitted_at":"2014-01-17T07:20:13Z","abstract_excerpt":"Let $(1)$ be an automorphism on an additive category $\\mathcal{B}$, and let $\\eta\\colon (1)\\to {\\rm Id}_{\\mathcal{B}}$ be a natural transformation satisfying $\\eta_{X(1)}=\\eta_X(1)$ for any object $X$ in $\\mathcal{B}$. We construct a new Frobenius exact structure on the category of complexes in $\\mathcal{B}$, which is associated to the natural transformation $\\eta$. As a consequence, the category introduced in Definition 2.4 of [J. Rickard, Morita theory for derived categories, J. London Math. Soc. 39(1989), 436-456] has a Frobenius exact structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4259","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"}