{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4B6OBJ2D6MJPUQBOYIJG3ABC3D","short_pith_number":"pith:4B6OBJ2D","schema_version":"1.0","canonical_sha256":"e07ce0a743f312fa402ec2126d8022d8ed88f79f2a49f9c4ee8c80c4451d64cb","source":{"kind":"arxiv","id":"1009.1166","version":4},"attestation_state":"computed","paper":{"title":"Functorial Data Migration","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.DB","authors_text":"David I. Spivak","submitted_at":"2010-09-06T21:05:23Z","abstract_excerpt":"In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three \"data migration functors\", which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection"},"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":"1009.1166","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DB","submitted_at":"2010-09-06T21:05:23Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"d4633dace5c8a223d8b3e809b29fee206b2b375f67c22c892ae927bc910d4625","abstract_canon_sha256":"d7643ad39c215ca54eabb2c23aa343b58308103bd05fe0c514fd502c6bc649b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:46.568927Z","signature_b64":"xMA4QjKwGc0G4AOo84mZKYF2a6PMJvH6SMoB+FQtki7lqjT6u2ZkvoXp7NlX1zH02SvRFwO9X3bqWkkLioP0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e07ce0a743f312fa402ec2126d8022d8ed88f79f2a49f9c4ee8c80c4451d64cb","last_reissued_at":"2026-05-18T03:34:46.568420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:46.568420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functorial Data Migration","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.DB","authors_text":"David I. Spivak","submitted_at":"2010-09-06T21:05:23Z","abstract_excerpt":"In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three \"data migration functors\", which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1166","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.1166","created_at":"2026-05-18T03:34:46.568501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.1166v4","created_at":"2026-05-18T03:34:46.568501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1166","created_at":"2026-05-18T03:34:46.568501+00:00"},{"alias_kind":"pith_short_12","alias_value":"4B6OBJ2D6MJP","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4B6OBJ2D6MJPUQBO","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4B6OBJ2D","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2112.05520","citing_title":"A category-theoretic approach to modeling John Cage's Silent piece","ref_index":40,"is_internal_anchor":true},{"citing_arxiv_id":"2604.04495","citing_title":"Kleisli semantics and hypergraph composition for Greimasian narrative programs","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15100","citing_title":"Presenting Neural Networks via Coherent Functors","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D","json":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D.json","graph_json":"https://pith.science/api/pith-number/4B6OBJ2D6MJPUQBOYIJG3ABC3D/graph.json","events_json":"https://pith.science/api/pith-number/4B6OBJ2D6MJPUQBOYIJG3ABC3D/events.json","paper":"https://pith.science/paper/4B6OBJ2D"},"agent_actions":{"view_html":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D","download_json":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D.json","view_paper":"https://pith.science/paper/4B6OBJ2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.1166&json=true","fetch_graph":"https://pith.science/api/pith-number/4B6OBJ2D6MJPUQBOYIJG3ABC3D/graph.json","fetch_events":"https://pith.science/api/pith-number/4B6OBJ2D6MJPUQBOYIJG3ABC3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D/action/storage_attestation","attest_author":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D/action/author_attestation","sign_citation":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D/action/citation_signature","submit_replication":"https://pith.science/pith/4B6OBJ2D6MJPUQBOYIJG3ABC3D/action/replication_record"}},"created_at":"2026-05-18T03:34:46.568501+00:00","updated_at":"2026-05-18T03:34:46.568501+00:00"}