{"paper":{"title":"On the Representation Categories of Weak Hopf Algebras Arising from Levin-Wen Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.CT","math.MP"],"primary_cat":"math.QA","authors_text":"Ansi Bai, Zhi-Hao Zhang","submitted_at":"2025-03-09T19:04:55Z","abstract_excerpt":"In their study of Levin-Wen models [Commun. Math. Phys. 313 (2012) 351-373], Kitaev and Kong proposed a weak Hopf algebra associated with a unitary fusion category $\\mathcal{C}$ and a unitary left $\\mathcal{C}$-module $\\mathcal{M}$, and sketched a proof that its representation category is monoidally equivalent to the unitary $\\mathcal{C}$-module functor category $\\mathrm{Fun}^{\\mathrm{u}}_{\\mathcal{C}}(\\mathcal{M},\\mathcal{M})^\\mathrm{rev}$. We give an independent proof of this result without the unitarity conditions. In particular, viewing $\\mathcal{C}$ as a left $\\mathcal{C} \\boxtimes \\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06731","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/2503.06731/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"}