{"paper":{"title":"Geometric constructions preserve fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Bertfried Fauser, Steven Vickers","submitted_at":"2014-11-10T15:27:26Z","abstract_excerpt":"Let $\\mathcal{C}$ be a representable 2-category, and $\\mathfrak{T}_\\bullet$ a 2-endofunctor of the arrow 2-category $\\mathcal{C}^\\downarrow$ such that (i) $\\mathsf{cod} \\mathfrak{T}_\\bullet = \\mathsf{cod}$ and (ii) $\\mathfrak{T}_\\bullet$ preserves proneness of morphisms in $\\mathcal{C}^\\downarrow$. Then $\\mathfrak{T}_\\bullet$ preserves fibrations and opfibrations in $\\mathcal{C}$.\n  The proof takes Street's characterization of (e.g.) opfibrations as pseudoalgebras for 2-monads $\\mathfrak{L}_B$ on slice categories $\\mathcal{C}/B$ and develops it by defining a 2-monad $\\mathfrak{L}_\\bullet$ on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2457","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"}