{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:I5IQXSAJPJ4DMFZ7725X3DCSPN","short_pith_number":"pith:I5IQXSAJ","schema_version":"1.0","canonical_sha256":"47510bc8097a7836173ffebb7d8c527b42912bc2a5f04517e706ef87bc6043f2","source":{"kind":"arxiv","id":"math/9802029","version":1},"attestation_state":"computed","paper":{"title":"Categorification","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"James Dolan, John C. Baez","submitted_at":"1998-02-05T19:25:50Z","abstract_excerpt":"Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in turn should satisfy certain equations of their own, called `coherence laws'. Iterating this process requires a theory of `n-categories', algebraic structures having objects, morphisms between objects, 2-morphisms between morphisms and so on up to n-morphisms. After a brief introduction to n-categories and their relation to homotopy theory, we discuss algebrai"},"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":"math/9802029","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1998-02-05T19:25:50Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"1902bbdb1e730d48389b9d186a92afc693398c97f2bab4b8bb384240a55a01bd","abstract_canon_sha256":"44f813b0102a09512cc8fe1062f36a398b8d11bcdcdcf1785442febb97127968"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:38.438205Z","signature_b64":"Vw63hy7JA4JVAM/AWlFJiJTT1cj+woiivNCnpsmWHY2UdqnieqqMENqDk2UX/rCW17e5Z6GUjsLhxoJQ5Y/HDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47510bc8097a7836173ffebb7d8c527b42912bc2a5f04517e706ef87bc6043f2","last_reissued_at":"2026-05-18T02:35:38.437698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:38.437698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categorification","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"James Dolan, John C. Baez","submitted_at":"1998-02-05T19:25:50Z","abstract_excerpt":"Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in turn should satisfy certain equations of their own, called `coherence laws'. Iterating this process requires a theory of `n-categories', algebraic structures having objects, morphisms between objects, 2-morphisms between morphisms and so on up to n-morphisms. After a brief introduction to n-categories and their relation to homotopy theory, we discuss algebrai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9802029","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":"math/9802029","created_at":"2026-05-18T02:35:38.437793+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9802029v1","created_at":"2026-05-18T02:35:38.437793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9802029","created_at":"2026-05-18T02:35:38.437793+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5IQXSAJPJ4D","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5IQXSAJPJ4DMFZ7","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5IQXSAJ","created_at":"2026-05-18T12:25:49.038998+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN","json":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN.json","graph_json":"https://pith.science/api/pith-number/I5IQXSAJPJ4DMFZ7725X3DCSPN/graph.json","events_json":"https://pith.science/api/pith-number/I5IQXSAJPJ4DMFZ7725X3DCSPN/events.json","paper":"https://pith.science/paper/I5IQXSAJ"},"agent_actions":{"view_html":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN","download_json":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN.json","view_paper":"https://pith.science/paper/I5IQXSAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9802029&json=true","fetch_graph":"https://pith.science/api/pith-number/I5IQXSAJPJ4DMFZ7725X3DCSPN/graph.json","fetch_events":"https://pith.science/api/pith-number/I5IQXSAJPJ4DMFZ7725X3DCSPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN/action/storage_attestation","attest_author":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN/action/author_attestation","sign_citation":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN/action/citation_signature","submit_replication":"https://pith.science/pith/I5IQXSAJPJ4DMFZ7725X3DCSPN/action/replication_record"}},"created_at":"2026-05-18T02:35:38.437793+00:00","updated_at":"2026-05-18T02:35:38.437793+00:00"}