{"paper":{"title":"Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Thibault D. D\\'ecoppet","submitted_at":"2025-06-19T11:57:11Z","abstract_excerpt":"Fix a finite symmetric tensor category $\\mathcal{E}$ over an algebraically closed field. We derive an $\\mathcal{E}$-enriched version of Shimizu's characterizations of non-degeneracy for finite braided tensor categories. In order to do so, we consider, associated to any $\\mathcal{E}$-enriched finite braided tensor category $\\mathcal{A}$ satisfying a mild technical assumption, a Hopf algebra $\\mathbb{F}_{\\mathcal{E}/\\mathcal{A}}$ in $\\mathcal{A}$. This is a generalization of Lyubashenko's universal Hopf algebra $\\mathbb{F}_{\\mathcal{A}}$ in $\\mathcal{A}$. In fact, we show that there is a short e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16241","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/2506.16241/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"}