{"paper":{"title":"On \\'Etale Algebras and Bosonic Fusion 2-Categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Hao Xu","submitted_at":"2024-11-20T14:48:34Z","abstract_excerpt":"We classify all connected and Lagrangian \\'etale algebras in the Drinfeld center $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$, where $G$ is a finite group and $\\pi$ is a 4-cocycle on $G$. By D\\'ecoppet's result every bosonic fusion 2-category $\\mathfrak{C}$ has its Drinfeld center equivalent to $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$ for some $G$ and $\\pi$. Combining this fact with classification of Lagrangian algebras in $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$, we obtain a classification of bosonic fusion 2-categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13367","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13367/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}