{"paper":{"title":"An equivalence between enriched $\\infty$-categories and $\\infty$-categories with weak action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Hadrian Heine","submitted_at":"2020-09-05T01:08:54Z","abstract_excerpt":"We show that an $\\infty$-category $\\mathcal{M}$ with a closed left action of a monoidal $\\infty$-category $\\mathcal{V}$ is completely determined by the $\\mathcal{V}$-valued graph of morphism objects equipped with the structure of a $\\mathcal{V}$-enrichment in the sense of Gepner-Haugseng. We prove a similar result when $\\mathcal{M}$ is a $\\mathcal{V}$-enriched $\\infty$-category in the sense of Lurie, an operadic generalization of the notion of $\\infty$-category with closed left action. Precisely, we prove that sending a $\\mathcal{V}$-enriched $\\infty$-category in the sense of Lurie to the $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02428","kind":"arxiv","version":5},"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/2009.02428/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"}