{"paper":{"title":"Dualizable presentable $\\infty$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.CT","authors_text":"Maxime Ramzi","submitted_at":"2024-10-28T21:03:52Z","abstract_excerpt":"We prove that for any presentably symmetric monoidal $\\infty$-category $\\mathcal{V}$, the $\\infty$-category $\\mathbf{Mod}_\\mathcal{V}(\\mathbf{Pr}^{\\mathrm{L}})^{\\mathrm{dbl}}$ of dualizable presentable $\\mathcal{V}$-modules and internal left adjoints between them is itself presentable.\n  Along the way, we survey formal properties of these dualizable $\\mathcal V$-modules. We pay close attention to the case of the $\\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21537","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/2410.21537/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"}