{"paper":{"title":"Invertible Fusion Categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Noah Snyder, Sean Sanford","submitted_at":"2024-07-02T18:36:11Z","abstract_excerpt":"A tensor category $\\mathcal{C}$ over a field $\\mathbb{K}$ is said to be invertible if there's a tensor category $\\mathcal{D}$ such that $\\mathcal{C}\\boxtimes\\mathcal{D}$ is Morita equivalent to $\\mathrm{Vec}_{\\mathbb{K}}$. When $\\mathbb{K}$ is algebraically closed, it is well-known that the only invertible fusion category is $\\mathrm{Vec}_{\\mathbb{K}}$, and any invertible multi-fusion category is Morita equivalent to $\\mathrm{Vec}_{\\mathbb{K}}$. By contrast, we show that for general $\\mathbb{K}$ the invertible multi-fusion categories over a field $\\mathbb{K}$ are classified (up to Morita equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02597","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/2407.02597/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"}