{"paper":{"title":"Gelfand spectra in Grothendieck toposes using geometric mathematics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CT","authors_text":"Bas Spitters (Universit\\'e Paris-Sud/INRIA Saclay), IMAPP), Sander Wolters (Radboud University Nijmegen, Steven Vickers (School of Computer Science, University of Birmingham)","submitted_at":"2013-10-02T13:50:28Z","abstract_excerpt":"In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A)  of sheaves on a locale and a commutative C*-algebra, a,  within that topos.  The Gelfand spectrum of a is a locale S in this topos, which is equivalent to a bundle over the base locale.  We further develop this external presentation of the locale S, by noting that the construction of the Gelfand spectrum in a general topos can be described using geometric logic.  As a consequence, the spectrum, seen as a bundle, is computed fibrewise.\n  As a by-produc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0705","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":""},"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"}