{"paper":{"title":"The factor set of Gr-categories of the type $(\\Pi,A)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nguyen Tien Quang","submitted_at":"2009-11-09T14:30:12Z","abstract_excerpt":"Any $\\Gamma$-graded categorical group is determined by a factor set of a categorical group. This paper studies the factor set of the group $\\Gamma$ with coefficients in the categorical group of the type $(\\Pi,A).$ Then, an interpretation of the notion of $\\Gamma-$operator $3-$cocycle is presented and the proof of cohomological classification theorem for the a $\\Gamma-$graded Gr-category is also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1689","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"}