{"paper":{"title":"Extension theory for braided-enriched fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Corey Jones, David Penneys, Julia Plavnik, Scott Morrison","submitted_at":"2019-10-08T02:37:00Z","abstract_excerpt":"For a braided fusion category $\\mathcal{V}$, a $\\mathcal{V}$-fusion category is a fusion category $\\mathcal{C}$ equipped with a braided monoidal functor $\\mathcal{F}:\\mathcal{V} \\to Z(\\mathcal{C})$. Given a fixed $\\mathcal{V}$-fusion category $(\\mathcal{C}, \\mathcal{F})$ and a fixed $G$-graded extension $\\mathcal{C}\\subseteq \\mathcal{D}$ as an ordinary fusion category, we characterize the enrichments $\\widetilde{\\mathcal{F}}:\\mathcal{V} \\to Z(\\mathcal{D})$ of $\\mathcal{D}$ which are compatible with the enrichment of $\\mathcal{C}$. We show that G-crossed extensions of a braided fusion category "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03178","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/1910.03178/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"}