{"paper":{"title":"Type refinement and monoidal closed bifibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL","math.CT"],"primary_cat":"cs.LO","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","submitted_at":"2013-10-01T12:13:52Z","abstract_excerpt":"The concept of_refinement_ in type theory is a way of reconciling the \"intrinsic\" and the \"extrinsic\" meanings of types. We begin with a rigorous analysis of this concept, settling on the simple conclusion that the type-theoretic notion of \"type refinement system\" may be identified with the category-theoretic notion of \"functor\". We then use this correspondence to give an equivalent type-theoretic formulation of Grothendieck's definition of (bi)fibration, and extend this to a definition of_monoidal closed bifibrations_, which we see as a natural space in which to study the properties of proofs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0263","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"}