{"paper":{"title":"A classifying localic category for locally compact locales","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Christopher Townsend","submitted_at":"2026-06-01T10:15:15Z","abstract_excerpt":"For an internal category $\\mathbb{C}$ in a cartesian category $\\mathcal{C}$ we define, naturally in objects $X$ of $\\mathcal{C}$, $Prin_{\\mathbb{C}}(X)$. This is a category whose objects are principal $c \\mathbb{C}$-bundles over $X$ and whose morphisms are principal $c(\\mathbb{C}^{\\uparrow})$-bundles. Here $c(\\_)$ denotes taking the core groupoid of a category (same objects but only isomorphisms as morphisms) and $\\mathbb{C}^{\\uparrow}$ is the arrow category of $\\mathbb{C}$ (objects are morphisms, morphisms are commuting squares). We show that $X \\mapsto Prin_{\\mathbb{C}}(X)$ is a stack of cat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02025","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/2606.02025/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"}