{"paper":{"title":"Duals and adjoints in higher Morita categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.QA"],"primary_cat":"math.CT","authors_text":"Claudia Scheimbauer, Owen Gwilliam","submitted_at":"2018-04-29T13:05:34Z","abstract_excerpt":"We study duals for objects and adjoints for $k$-morphisms in $\\operatorname{Alg}_n(\\mathcal{S})$, an $(\\infty,n+N)$-category that models a higher Morita category for $E_n$ algebra objects in a symmetric monoidal $(\\infty,N)$-category $\\mathcal{S}$. Our model of $\\operatorname{Alg}(\\mathcal{S})$ uses the geometrically convenient framework of factorization algebras. The main result is that $\\operatorname{Alg}_n(\\mathcal{S})$ is fully $n$-dualizable, verifying a conjecture of Lurie. Moreover, we unpack the consequences for a natural class of fully extended topological field theories and explore $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10924","kind":"arxiv","version":2},"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"}