{"paper":{"title":"Deformation Theory for $(\\infty,n)$-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Roman Kositsyn","submitted_at":"2025-04-23T00:00:40Z","abstract_excerpt":"For an $(\\infty,n)$-category $\\mathscr E$ we define an $(\\infty,1)$ category $\\mathrm{TwAr}(\\mathscr E)$ and provide an isomorphism between the stabilization of the overcategory of $\\mathscr E$ in $\\mathrm{Cat}_{(\\infty,n)}$ and the $\\infty$-category of spectrum-valued functors on $\\mathrm{TwAr}(\\mathscr E)$. We use this to develop the deformation theory of $(\\infty,n)$-categories and apply it to given an $\\infty$-categorical characterization of lax-idempotent monads."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16326","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/2504.16326/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"}