{"paper":{"title":"Skew category algebras and modules on ringed finite sites","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Fei Xu, Mawei Wu","submitted_at":"2022-07-11T09:26:03Z","abstract_excerpt":"Let $\\mathcal{C}$ be a small category. We investigate ringed sites $(\\mathbf{C},\\mathfrak{R})$ on $\\mathcal{C}$ and the resulting module categories $\\mathfrak{M}{\\rm od}\\text{-}\\mathfrak{R}$. When $\\mathcal{C}$ is finite, based on Grothendieck and Verdier's classification of finite topoi, we prove that each $\\mathfrak{M}{\\rm od}\\text{-}\\mathfrak{R}$ is equivalent to ${\\rm Mod}\\text{-}\\mathfrak{R}|_{\\mathcal{D}}[\\mathcal{D}]$, where $\\mathfrak{R}|_{\\mathcal{D}}[\\mathcal{D}]$ is the skew category algebra, canonically defined on $(\\mathbf{C},\\mathfrak{R})$, for a uniquely determined full subcateg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.04731","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/2207.04731/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"}