{"paper":{"title":"A characterization of sheaves among six functor formalisms on $\\mathrm{LCH}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AT","authors_text":"Marco Volpe, Ulrich Bunke","submitted_at":"2026-06-09T06:00:52Z","abstract_excerpt":"Let $\\mathcal{C}$ be any stable presentably symmetric monoidal $\\infty$-category. In this paper, we characterize $\\mathrm{Shv}(-,\\mathcal{C})$ on locally compact Hausdorff spaces as the unique six functor formalism satisfying a list of very natural properties. As a consequence, we deduce that every continuous six functor formalism $D$ in the sense of Zhu is equivalent to $\\mathrm{Shv}(-, D(\\mathrm{pt}))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10453","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/2606.10453/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"}