{"paper":{"title":"Categorical quantum symmetries and ribbon tensor 2-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Hank Chen","submitted_at":"2025-01-14T11:46:37Z","abstract_excerpt":"In a companion work on the combinatorial quantization of 4d 2-Chern-Simons theory, the author has constructed the Hopf category of quantum 2-gauge transformations $\\tilde{C}=\\mathbb{U}_q\\mathfrak{G}$ acting on the discrete surface-holonomy configurations on a lattice. We prove in this article that the 2-$\\mathsf{Hilb}$-enriched 2-representation 2-category $\\operatorname{2Rep}(\\tilde C)$ of finite semisimple $\\mathbb{C}$-linear $\\tilde C$-module categories is braided, planar-pivotal, and lax rigid, hence $\\operatorname{2Rep}(\\tilde C)$ provides an example of a ribbon tensor 2-category. We expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08041/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"}