{"paper":{"title":"Fibrations of AU-contexts beget fibrations of toposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Sina Hazratpour, Steven Vickers","submitted_at":"2018-08-24T19:59:31Z","abstract_excerpt":"Suppose an extension map $U\\colon \\mathbb{T}_1 \\to \\mathbb{T}_0$ in the 2-category $\\mathfrak{Con}$ of contexts for arithmetic universes satisfies a Chevalley criterion for being an (op)fibration in $\\mathfrak{Con}$. If $M$ is a model of $\\mathbb{T}_0$ in an elementary topos $\\mathcal{S}$ with nno, then the classifier $p\\colon\\mathcal{S}[\\mathbb{T}_1/M]\\to\\mathcal{S}$ satisfies Johnstone's criterion for being an (op)fibration in the 2-category $\\mathcal{E}\\mathfrak{Top}$ of elementary toposes (with nno) and geometric morphisms. Along the way, we provide a convenient reformulation of Johnstone'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08291","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":""},"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"}