{"paper":{"title":"Presentable $(\\infty, n)$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Germ\\'an Stefanich","submitted_at":"2020-11-05T18:49:24Z","abstract_excerpt":"We define for each $n \\geq 1$ a symmetric monoidal $(\\infty, n+1)$-category $n\\mathrm{Pr}^L$ whose objects we call presentable $(\\infty,n)$-categories, generalizing the usual theory of presentable $(\\infty,1)$-categories. We show that each object $\\mathcal{C}$ in $n\\mathrm{Pr}^L$ has an underlying $(\\infty,n)$-category $\\psi_n(\\mathcal{C})$ which admits all conical colimits, and that conical colimits of right adjointable diagrams in $\\psi_n(\\mathcal{C})$ can be computed in terms of conical limits after passage to right adjoints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03035","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/2011.03035/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"}