{"paper":{"title":"Freely adjoining monoidal duals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Kevin Coulembier, Michel Van den Bergh, Ross Street","submitted_at":"2020-04-21T01:09:37Z","abstract_excerpt":"Given a monoidal category $\\mathscr{C}$ with an object $J$, we construct a monoidal category $\\mathscr{C}[J^{\\vee}]$ by freely adjoining a right dual $J^{\\vee}$ to $J$. We show that the canonical strong monoidal functor $\\Omega : \\mathscr{C}\\to \\mathscr{C}[J^{\\vee}]$ provides the unit for a biadjunction with the forgetful 2-functor from the 2-category of monoidal categories with a distinguished dual pair to the 2-category of monoidal categories with a distinguished object. We show that $\\Omega : \\mathscr{C}\\to \\mathscr{C}[J^{\\vee}]$ is fully faithful and provide coend formulas for homs of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.09697","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/2004.09697/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"}