{"paper":{"title":"The pivotal cover and Frobenius-Schur indicators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Kenichi Shimizu","submitted_at":"2013-09-18T05:22:54Z","abstract_excerpt":"In this paper, we introduce the notion of the pivotal cover $\\mathcal{C}^{\\mathsf{piv}}$ of a left rigid monoidal category $\\mathcal{C}$ to develop a theoretical foundation for the theory of Frobenius-Schur (FS) indicators in \"non-pivotal\" settings. For an object $\\mathbf{V} \\in \\mathcal{C}^{\\mathsf{piv}}$, the $(n, r)$-th FS indicator $\\nu_{n, r}(\\mathbf{V})$ is defined by generalizing that of an object of a pivotal monoidal category. This notion gives a categorical viewpoint to some recent results on generalizations of FS indicators.\n  Based on our framework, we also study the FS indicators "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4539","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}