{"paper":{"title":"Fusion and monodromy in the Temperley-Lieb category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"Jonathan Bellet\\^ete, Yvan Saint-Aubin","submitted_at":"2018-02-26T08:53:03Z","abstract_excerpt":"Graham and Lehrer (1998) introduced a Temperley-Lieb category $\\mathsf{\\widetilde{TL}}$ whose objects are the non-negative integers and the morphisms in $\\mathsf{Hom}(n,m)$ are the link diagrams from $n$ to $m$ nodes. The Temperley-Lieb algebra $\\mathsf{TL}_{n}$ is identified with $\\mathsf{Hom}(n,n)$. The category $\\mathsf{\\widetilde{TL}}$ is shown to be monoidal. We show that it is also a braided category by constructing explicitly a commutor. A twist is also defined on $\\mathsf{\\widetilde{TL}}$. We introduce a module category ${\\text{ Mod}_{\\mathsf{\\widetilde{TL}}}}$ whose objects are functo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09203","kind":"arxiv","version":3},"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"}