{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WO4A7XV33VEOYDRQ5XLBSBDPDY","short_pith_number":"pith:WO4A7XV3","schema_version":"1.0","canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","source":{"kind":"arxiv","id":"1401.7748","version":1},"attestation_state":"computed","paper":{"title":"Non-Simplicial Nerves for Two-Dimensional Categorical Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Nathaniel Watson","submitted_at":"2014-01-30T05:47:11Z","abstract_excerpt":"The most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it is a quasicategory which has unique fillers for inner horns of dimension $3$ and greater. Using Duskin's technique, we show how his nerve applies to $(2,1)$-category functors, making it a fully faithful inclusion of $(2,1)$-categories into simplicial sets. Then we consider analogues of this extension of Duskin's result for several different two-dimensional "},"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":"1401.7748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"10292ea620b823adda3a5ff7f82ea8d9ea4ae0a392642e62f0e252950bc462b4","abstract_canon_sha256":"66355ce230d3a4ac061b4a5dab492dfc22c69b52a9d4948ce4f689cd40f65172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:38.565173Z","signature_b64":"gv7dQl7elSVLDCMhOVfMNT1A/oFVuuMtYWgldGDSIWtIQLPzHX4Te5D8sneP/id+pyXwCO4gmVvAbIxbOVmkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","last_reissued_at":"2026-05-18T03:00:38.564336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:38.564336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Simplicial Nerves for Two-Dimensional Categorical Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Nathaniel Watson","submitted_at":"2014-01-30T05:47:11Z","abstract_excerpt":"The most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it is a quasicategory which has unique fillers for inner horns of dimension $3$ and greater. Using Duskin's technique, we show how his nerve applies to $(2,1)$-category functors, making it a fully faithful inclusion of $(2,1)$-categories into simplicial sets. Then we consider analogues of this extension of Duskin's result for several different two-dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7748","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":"1401.7748","created_at":"2026-05-18T03:00:38.564482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7748v1","created_at":"2026-05-18T03:00:38.564482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7748","created_at":"2026-05-18T03:00:38.564482+00:00"},{"alias_kind":"pith_short_12","alias_value":"WO4A7XV33VEO","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WO4A7XV33VEOYDRQ","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WO4A7XV3","created_at":"2026-05-18T12:28:54.890064+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/WO4A7XV33VEOYDRQ5XLBSBDPDY","json":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY.json","graph_json":"https://pith.science/api/pith-number/WO4A7XV33VEOYDRQ5XLBSBDPDY/graph.json","events_json":"https://pith.science/api/pith-number/WO4A7XV33VEOYDRQ5XLBSBDPDY/events.json","paper":"https://pith.science/paper/WO4A7XV3"},"agent_actions":{"view_html":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY","download_json":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY.json","view_paper":"https://pith.science/paper/WO4A7XV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7748&json=true","fetch_graph":"https://pith.science/api/pith-number/WO4A7XV33VEOYDRQ5XLBSBDPDY/graph.json","fetch_events":"https://pith.science/api/pith-number/WO4A7XV33VEOYDRQ5XLBSBDPDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/action/storage_attestation","attest_author":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/action/author_attestation","sign_citation":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/action/citation_signature","submit_replication":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/action/replication_record"}},"created_at":"2026-05-18T03:00:38.564482+00:00","updated_at":"2026-05-18T03:00:38.564482+00:00"}