{"paper":{"title":"Structure of Ann-Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nguyen Tien Quang","submitted_at":"2008-04-11T01:08:52Z","abstract_excerpt":"This paper presents the structure conversion by which from an Ann-category $\\A,$ we can obtain its reduced Ann-category of the type $(R,M)$ whose structure is a family of five functions $k=(\\xi,\\eta,\\alpha,\\lambda,\\rho)$. Then we will show that each Ann-category is determined by three invariants:\n  1. The ring $\\Pi_0(\\A)$ of the isomorphic classes of objects of $\\A$,\n  2. $\\Pi_0(\\A)$-bimodule $\\Pi_1(\\A) = \\Aut_{\\A}(0),$\n  3. The element $ \\bar{k}\\in H^{3}_{M}(\\Pi_0(\\A), \\Pi_1(\\A))$ (the ring cohomology due to MacLane)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1820","kind":"arxiv","version":2},"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"}