{"paper":{"title":"Completion for braided enriched monoidal categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CT","authors_text":"David Penneys, Julia Plavnik, Scott Morrison","submitted_at":"2018-09-26T02:18:35Z","abstract_excerpt":"Monoidal categories enriched in a braided monoidal category $\\mathcal{V}$ are classified by braided oplax monoidal functors from $\\mathcal{V}$ to the Drinfeld centers of ordinary monoidal categories. In this article, we prove that this classifying functor is strongly monoidal if and only if the original $\\mathcal{V}$-monoidal category is tensored over $\\mathcal{V}$. We then define a completion operation which produces a tensored $\\mathcal{V}$-monoidal category $\\overline{\\mathcal{C}}$ from an arbitrary $\\mathcal{V}$-monoidal category $\\mathcal{C}$, and we determine many equivalent conditions w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09782","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"}