{"paper":{"title":"Relative tensor products and Koszul duality in monoidal oo-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Asaf Horev, Ishai Dan-Cohen","submitted_at":"2022-10-21T10:31:44Z","abstract_excerpt":"This semi-expository work covers central aspects of the theory of relative tensor products as developed in Higher Algebra, as well as their application to Koszul duality for algebras in monoidal oo-categories. Part of our goal is to expand on the rather condensed account of loc. cit. Along the way, we generalize various aspects of the theory. For instance, given a monoidal oo-category Cc, an oo-category Mm which is left-tensored over Cc, and an algebra A in Cc, we construct an action of A-A-bimodules N in Cc on left A-modules M in Mm by an \"external relative tensor product\" N \\otimes_A M. (Up "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.11861","kind":"arxiv","version":4},"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/2210.11861/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"}