{"paper":{"title":"Continuous six-functor formalism on locally compact Hausdorff spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.KT","authors_text":"Qingchong Zhu","submitted_at":"2025-07-17T21:11:05Z","abstract_excerpt":"We show that the functor sending a locally compact Hausdorff space $X$ to the $\\infty$-category of spectral sheaves $\\mathrm{Shv}(X; \\mathrm{Sp})$ is initial among all continuous six-functor formalisms on the category of locally compact Hausdorff spaces. Here, continuous six-functor formalisms are those valued in dualizable presentable stable $\\infty$-categories and satisfying canonical descent, profinite descent, and hyperdescent. As an application, we generalize Efimov's computation of the algebraic $K$-theory of sheaves to all localizing invariants on continuous six-functor formalisms. Our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13537","kind":"arxiv","version":2},"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/2507.13537/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"}