{"paper":{"title":"Descent for sheaves on compact Hausdorff spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Peter J. Haine","submitted_at":"2022-10-01T04:11:20Z","abstract_excerpt":"These notes explain some descent results for $\\infty$-categories of sheaves on compact Hausdorff spaces and derive some consequences. Specifically, given a compactly assembled $\\infty$-category $\\mathcal{E}$, we show that the functor sending a locally compact Hausdorff space $X$ to the $\\infty$-category $\\operatorname{Sh}^{\\operatorname{post}}(X;\\mathcal{E})$ of Postnikov complete $\\mathcal{E}$-valued sheaves on $ X $ satisfies descent for proper surjections. This implies proper descent for left complete derived $\\infty$-categories and that the functor $\\operatorname{Sh}^{\\operatorname{post}}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.00186","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/2210.00186/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"}