{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H7NV4AWMBL5LMQBVXLEENGLJCO","short_pith_number":"pith:H7NV4AWM","schema_version":"1.0","canonical_sha256":"3fdb5e02cc0afab64035bac84699691399f90540b1f992c544dda49bb4ee1fc8","source":{"kind":"arxiv","id":"1506.05500","version":3},"attestation_state":"computed","paper":{"title":"Fibrations and Yoneda's lemma in an $\\infty$-cosmos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Dominic Verity, Emily Riehl","submitted_at":"2015-06-17T21:22:08Z","abstract_excerpt":"We use the terms $\\infty$-categories and $\\infty$-functors to mean the objects and morphisms in an $\\infty$-cosmos: a simplicially enriched category satisfying a few axioms, reminiscent of an enriched category of fibrant objects. Quasi-categories, Segal categories, complete Segal spaces, marked simplicial sets, iterated complete Segal spaces, $\\theta_n$-spaces, and fibered versions of each of these are all $\\infty$-categories in this sense. Previous work in this series shows that the basic category theory of $\\infty$-categories and $\\infty$-functors can be developed only in reference to the ax"},"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":"1506.05500","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-06-17T21:22:08Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f0e25b5139079519e1f27dab76bcc14c7ae68847e95fe99c7c03608de867aab3","abstract_canon_sha256":"0d1dd1f656d9e38b3cc009851f0eb6588cc97f974695fd3129587175778b0737"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.274021Z","signature_b64":"W60mHtU9zDGMzOU3hCf+ozyMP41yZH+tcAtyN6kuzVLL87F38usgw2zAVifmhzmstCwGJ7m65g+dAS/VV67bBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fdb5e02cc0afab64035bac84699691399f90540b1f992c544dda49bb4ee1fc8","last_reissued_at":"2026-05-18T01:12:36.273417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.273417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibrations and Yoneda's lemma in an $\\infty$-cosmos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Dominic Verity, Emily Riehl","submitted_at":"2015-06-17T21:22:08Z","abstract_excerpt":"We use the terms $\\infty$-categories and $\\infty$-functors to mean the objects and morphisms in an $\\infty$-cosmos: a simplicially enriched category satisfying a few axioms, reminiscent of an enriched category of fibrant objects. Quasi-categories, Segal categories, complete Segal spaces, marked simplicial sets, iterated complete Segal spaces, $\\theta_n$-spaces, and fibered versions of each of these are all $\\infty$-categories in this sense. Previous work in this series shows that the basic category theory of $\\infty$-categories and $\\infty$-functors can be developed only in reference to the ax"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05500","kind":"arxiv","version":3},"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":"1506.05500","created_at":"2026-05-18T01:12:36.273514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.05500v3","created_at":"2026-05-18T01:12:36.273514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05500","created_at":"2026-05-18T01:12:36.273514+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7NV4AWMBL5L","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7NV4AWMBL5LMQBV","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7NV4AWM","created_at":"2026-05-18T12:29:22.688609+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/H7NV4AWMBL5LMQBVXLEENGLJCO","json":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO.json","graph_json":"https://pith.science/api/pith-number/H7NV4AWMBL5LMQBVXLEENGLJCO/graph.json","events_json":"https://pith.science/api/pith-number/H7NV4AWMBL5LMQBVXLEENGLJCO/events.json","paper":"https://pith.science/paper/H7NV4AWM"},"agent_actions":{"view_html":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO","download_json":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO.json","view_paper":"https://pith.science/paper/H7NV4AWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.05500&json=true","fetch_graph":"https://pith.science/api/pith-number/H7NV4AWMBL5LMQBVXLEENGLJCO/graph.json","fetch_events":"https://pith.science/api/pith-number/H7NV4AWMBL5LMQBVXLEENGLJCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO/action/storage_attestation","attest_author":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO/action/author_attestation","sign_citation":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO/action/citation_signature","submit_replication":"https://pith.science/pith/H7NV4AWMBL5LMQBVXLEENGLJCO/action/replication_record"}},"created_at":"2026-05-18T01:12:36.273514+00:00","updated_at":"2026-05-18T01:12:36.273514+00:00"}