{"paper":{"title":"Crossed actions of matched pairs of groups on tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Sonia Natale","submitted_at":"2014-05-27T16:26:13Z","abstract_excerpt":"We introduce the notion of $(G, \\Gamma)$-crossed action on a tensor category, where $(G, \\Gamma)$ is a matched pair of finite groups. A tensor category is called a $(G, \\Gamma)$-crossed tensor category if it is endowed with a $(G, \\Gamma)$-crossed action. We show that every $(G, \\Gamma)$-crossed tensor category $\\mathcal C$ gives rise to a tensor category $\\mathcal C^{(G, \\Gamma)}$ that fits into an exact sequence of tensor categories $\\operatorname{Rep G} \\to \\mathcal C^{(G, \\Gamma)} \\to \\mathcal C$. We also define the notion of a $(G, \\Gamma)$-braiding in a $(G, \\Gamma)$-crossed tensor categ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6970","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"}