{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7QPF4MTVSQI2ZIIPRME43BDYMM","short_pith_number":"pith:7QPF4MTV","schema_version":"1.0","canonical_sha256":"fc1e5e32759411aca10f8b09cd8478633484ea263c8b23f3da0fdccd242cebdf","source":{"kind":"arxiv","id":"1904.00827","version":2},"attestation_state":"computed","paper":{"title":"Categories with Families: Unityped, Simply Typed, and Dependently Typed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Peter Dybjer, Pierre Clairambault, Simon Castellan","submitted_at":"2019-04-01T13:12:25Z","abstract_excerpt":"We show how the categorical logic of untyped, simply typed and dependently typed lambda calculus can be structured around the notion of category with family (cwf). To this end we introduce subcategories of simply typed cwfs (scwfs), where types do not depend on variables, and unityped cwfs (ucwfs), where there is only one type. We prove several equivalence and biequivalence theorems between cwf-based notions and basic notions of categorical logic, such as cartesian operads, Lawvere theories, categories with finite products and limits, cartesian closed categories, and locally cartesian closed c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.00827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-01T13:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"bf3bfbac2dafe911d0ed98e7a7b4803066306775c5f0324f09dc6c2f02595f56","abstract_canon_sha256":"cec6f61c8024da614085f4e802c8f027aace688e8c64183982fab772a8655943"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:16:38.560746Z","signature_b64":"VXlhxISLP1ZglYyq92AY7aE1eDg9QItEIvsmfZ9dhQoRS1MZT+so3ed2K35swSKSZn5tcyP+4rZLutl2FR/pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc1e5e32759411aca10f8b09cd8478633484ea263c8b23f3da0fdccd242cebdf","last_reissued_at":"2026-07-05T01:16:38.560273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:16:38.560273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categories with Families: Unityped, Simply Typed, and Dependently Typed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Peter Dybjer, Pierre Clairambault, Simon Castellan","submitted_at":"2019-04-01T13:12:25Z","abstract_excerpt":"We show how the categorical logic of untyped, simply typed and dependently typed lambda calculus can be structured around the notion of category with family (cwf). To this end we introduce subcategories of simply typed cwfs (scwfs), where types do not depend on variables, and unityped cwfs (ucwfs), where there is only one type. We prove several equivalence and biequivalence theorems between cwf-based notions and basic notions of categorical logic, such as cartesian operads, Lawvere theories, categories with finite products and limits, cartesian closed categories, and locally cartesian closed c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00827","kind":"arxiv","version":2},"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/1904.00827/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.00827","created_at":"2026-07-05T01:16:38.560340+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.00827v2","created_at":"2026-07-05T01:16:38.560340+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00827","created_at":"2026-07-05T01:16:38.560340+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QPF4MTVSQI2","created_at":"2026-07-05T01:16:38.560340+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QPF4MTVSQI2ZIIP","created_at":"2026-07-05T01:16:38.560340+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QPF4MTV","created_at":"2026-07-05T01:16:38.560340+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.21225","citing_title":"Custom Representations of Inductive Families","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM","json":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM.json","graph_json":"https://pith.science/api/pith-number/7QPF4MTVSQI2ZIIPRME43BDYMM/graph.json","events_json":"https://pith.science/api/pith-number/7QPF4MTVSQI2ZIIPRME43BDYMM/events.json","paper":"https://pith.science/paper/7QPF4MTV"},"agent_actions":{"view_html":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM","download_json":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM.json","view_paper":"https://pith.science/paper/7QPF4MTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.00827&json=true","fetch_graph":"https://pith.science/api/pith-number/7QPF4MTVSQI2ZIIPRME43BDYMM/graph.json","fetch_events":"https://pith.science/api/pith-number/7QPF4MTVSQI2ZIIPRME43BDYMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM/action/storage_attestation","attest_author":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM/action/author_attestation","sign_citation":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM/action/citation_signature","submit_replication":"https://pith.science/pith/7QPF4MTVSQI2ZIIPRME43BDYMM/action/replication_record"}},"created_at":"2026-07-05T01:16:38.560340+00:00","updated_at":"2026-07-05T01:16:38.560340+00:00"}