{"paper":{"title":"Categories with dependent arrows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Iosif Petrakis","submitted_at":"2023-03-26T15:18:02Z","abstract_excerpt":"We present an abstract, categorical formulation of dependent functions in a fundamental manner and independently from the Sigma-construction. For that, we define first the notion of a category with family-arrows, or a $\\f$-category. A $(\\f, \\Sigma)$-category is a $\\f$-category with Sigma-objects, where a $(\\f, \\Sigma)$-category with a terminal object is exactly a type-category of Pitts, or a category with attributes of Cartmell. We introduce categories with dependent arrows, or $\\di$-categories, and we show that every $(\\f, \\Sigma)$-category is a $\\di$-category in a canonical way. The notion o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.14754","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/2303.14754/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"}