{"paper":{"title":"Exponentiable Higher Toposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Damien Lejay, Mathieu Anel","submitted_at":"2018-02-28T14:17:52Z","abstract_excerpt":"We characterise the class of exponentiable $\\infty$-toposes: $\\mathcal X$ is exponentiable if and only if $\\mathcal S\\mathrm{h}(\\mathcal X)$ is a continuous $\\infty$-category. The heart of the proof is the description of the $\\infty$-category of $\\mathcal C$-valued sheaves on $\\mathcal X$ as an $\\infty$-category of functors that satisfy finite limits conditions as well as filtered colimits conditions (instead of limits conditions purely); we call such functors $\\omega$-continuous sheaves.\n  As an application, we show that when $\\mathcal X$ is exponentiable, its $\\infty$-category of stable shea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10425","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":""},"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"}