{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:STRGJ7H37HJRTIXVY7XQLQDXVH","short_pith_number":"pith:STRGJ7H3","schema_version":"1.0","canonical_sha256":"94e264fcfbf9d319a2f5c7ef05c077a9daaf7ef9d94edc9d2f56b5c83f46c39f","source":{"kind":"arxiv","id":"1112.3456","version":1},"attestation_state":"computed","paper":{"title":"The Biequivalence of Locally Cartesian Closed Categories and Martin-L\\\"of Type Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Peter Dybjer (CSE), Pierre Clairambault","submitted_at":"2011-12-15T09:32:25Z","abstract_excerpt":"Seely's paper \"Locally cartesian closed categories and type theory\" contains a well-known result in categorical type theory: that the category of locally cartesian closed categories is equivalent to the category of Martin-L\\\"of type theories with Pi-types, Sigma-types and extensional identity types. However, Seely's proof relies on the problematic assumption that substitution in types can be interpreted by pullbacks. Here we prove a corrected version of Seely's theorem: that the B\\'enabou-Hofmann interpretation of Martin-L\\\"of type theory in locally cartesian closed categories yields a biequiv"},"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":"1112.3456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-12-15T09:32:25Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"ea6bbfad49ba9e4d06e5faa1694d866a8f6df0642acca2816aabe3d3256e4ea8","abstract_canon_sha256":"19c5258d2ef5504784547a12465a22ae3fef2e63500df6258c2ef8a4d5c9128f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.046897Z","signature_b64":"EfaL5uIOIPPF5yOsays2CetBr0HzNX7y53jyRyMGerVIJZYh9e8K9ceFGV/h/iEoPjNq1zMiHmCg1R0Ti6uzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e264fcfbf9d319a2f5c7ef05c077a9daaf7ef9d94edc9d2f56b5c83f46c39f","last_reissued_at":"2026-05-17T23:53:19.045863Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.045863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Biequivalence of Locally Cartesian Closed Categories and Martin-L\\\"of Type Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Peter Dybjer (CSE), Pierre Clairambault","submitted_at":"2011-12-15T09:32:25Z","abstract_excerpt":"Seely's paper \"Locally cartesian closed categories and type theory\" contains a well-known result in categorical type theory: that the category of locally cartesian closed categories is equivalent to the category of Martin-L\\\"of type theories with Pi-types, Sigma-types and extensional identity types. However, Seely's proof relies on the problematic assumption that substitution in types can be interpreted by pullbacks. Here we prove a corrected version of Seely's theorem: that the B\\'enabou-Hofmann interpretation of Martin-L\\\"of type theory in locally cartesian closed categories yields a biequiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3456","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.3456","created_at":"2026-05-17T23:53:19.046085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3456v1","created_at":"2026-05-17T23:53:19.046085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3456","created_at":"2026-05-17T23:53:19.046085+00:00"},{"alias_kind":"pith_short_12","alias_value":"STRGJ7H37HJR","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"STRGJ7H37HJRTIXV","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"STRGJ7H3","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.19946","citing_title":"Comparing semantic frameworks for dependently-sorted algebraic theories","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH","json":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH.json","graph_json":"https://pith.science/api/pith-number/STRGJ7H37HJRTIXVY7XQLQDXVH/graph.json","events_json":"https://pith.science/api/pith-number/STRGJ7H37HJRTIXVY7XQLQDXVH/events.json","paper":"https://pith.science/paper/STRGJ7H3"},"agent_actions":{"view_html":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH","download_json":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH.json","view_paper":"https://pith.science/paper/STRGJ7H3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3456&json=true","fetch_graph":"https://pith.science/api/pith-number/STRGJ7H37HJRTIXVY7XQLQDXVH/graph.json","fetch_events":"https://pith.science/api/pith-number/STRGJ7H37HJRTIXVY7XQLQDXVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH/action/storage_attestation","attest_author":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH/action/author_attestation","sign_citation":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH/action/citation_signature","submit_replication":"https://pith.science/pith/STRGJ7H37HJRTIXVY7XQLQDXVH/action/replication_record"}},"created_at":"2026-05-17T23:53:19.046085+00:00","updated_at":"2026-05-17T23:53:19.046085+00:00"}