{"paper":{"title":"Linear structures on locales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Jo\\~ao Paulo Santos, Pedro Resende","submitted_at":"2016-03-21T14:28:11Z","abstract_excerpt":"We define a notion of morphism for quotient vector bundles that yields both a category $\\textit{QVBun}$ and a contravariant global sections functor $C:\\textit{QVBun}^{\\textrm{op}}\\to\\textit{Vect}$ whose restriction to trivial vector bundles with fiber $F$ coincides with the contravariant functor $\\textit{Top}^{\\textrm{op}}\\to\\textit{Vect}$ of $F$-valued continuous functions. Based on this we obtain a linear extension of the adjunction between the categories of topological spaces and locales: (i) a linearized topological space is a spectral vector bundle, by which is meant a mildly restricted t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06435","kind":"arxiv","version":6},"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"}