{"paper":{"title":"Categorified trace for module tensor categories over braided tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Andr\\'e Henriques, David Penneys, James Tener","submitted_at":"2015-09-09T20:18:39Z","abstract_excerpt":"Given a braided pivotal category $\\mathcal C$ and a pivotal module tensor category $\\mathcal M$, we define a functor $\\mathrm{Tr}_{\\mathcal C}:\\mathcal M \\to \\mathcal C$, called the associated categorified trace. By a result of Bezrukavnikov, Finkelberg and Ostrik, the functor $\\mathrm{Tr}_{\\mathcal C}$ comes equipped with natural isomorphisms $\\tau_{x,y}:\\mathrm{Tr}_{\\mathcal C}(x \\otimes y) \\to \\mathrm{Tr}_{\\mathcal C}(y \\otimes x)$, which we call the traciators. This situation lends itself to a diagramatic calculus of `strings on cylinders', where the traciator corresponds to wrapping a str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02937","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":""},"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"}