{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:WHAFZAMXT5BWAQMAAZ6M5G6RE3","short_pith_number":"pith:WHAFZAMX","schema_version":"1.0","canonical_sha256":"b1c05c81979f43604180067cce9bd126ff81e1e3ba684800c7004997d755e96e","source":{"kind":"arxiv","id":"0808.4108","version":2},"attestation_state":"computed","paper":{"title":"A Thomason Model Structure on the Category of Small n-fold Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Simona Paoli, Thomas M. Fiore","submitted_at":"2008-08-29T15:09:18Z","abstract_excerpt":"We construct a cofibrantly generated Quillen model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. This is an n-fold analogue to Thomason's Quillen model structure on Cat. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, we completely prove that the un"},"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":"0808.4108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-29T15:09:18Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e09b870ea97abb132a0cc647c474ce62008a07ff1dadd4366b1bef799ba5cdb6","abstract_canon_sha256":"0cfb28c9eef603880b2cf62d42b215d646cb4029a1da5bf11630208dfdc6216e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.542385Z","signature_b64":"n6TlEml4xPF+t4C8xIuhh9DINJljGyFEwrR++xkUMZMN9q9KrrQojP3DcLPqIFczg6bFWj3DxJy90JnsAoroCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1c05c81979f43604180067cce9bd126ff81e1e3ba684800c7004997d755e96e","last_reissued_at":"2026-05-18T02:41:51.541908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.541908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Thomason Model Structure on the Category of Small n-fold Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Simona Paoli, Thomas M. Fiore","submitted_at":"2008-08-29T15:09:18Z","abstract_excerpt":"We construct a cofibrantly generated Quillen model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. This is an n-fold analogue to Thomason's Quillen model structure on Cat. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, we completely prove that the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.4108","kind":"arxiv","version":2},"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":"0808.4108","created_at":"2026-05-18T02:41:51.541982+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.4108v2","created_at":"2026-05-18T02:41:51.541982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.4108","created_at":"2026-05-18T02:41:51.541982+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHAFZAMXT5BW","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHAFZAMXT5BWAQMA","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHAFZAMX","created_at":"2026-05-18T12:25:58.018023+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/WHAFZAMXT5BWAQMAAZ6M5G6RE3","json":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3.json","graph_json":"https://pith.science/api/pith-number/WHAFZAMXT5BWAQMAAZ6M5G6RE3/graph.json","events_json":"https://pith.science/api/pith-number/WHAFZAMXT5BWAQMAAZ6M5G6RE3/events.json","paper":"https://pith.science/paper/WHAFZAMX"},"agent_actions":{"view_html":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3","download_json":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3.json","view_paper":"https://pith.science/paper/WHAFZAMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.4108&json=true","fetch_graph":"https://pith.science/api/pith-number/WHAFZAMXT5BWAQMAAZ6M5G6RE3/graph.json","fetch_events":"https://pith.science/api/pith-number/WHAFZAMXT5BWAQMAAZ6M5G6RE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3/action/storage_attestation","attest_author":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3/action/author_attestation","sign_citation":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3/action/citation_signature","submit_replication":"https://pith.science/pith/WHAFZAMXT5BWAQMAAZ6M5G6RE3/action/replication_record"}},"created_at":"2026-05-18T02:41:51.541982+00:00","updated_at":"2026-05-18T02:41:51.541982+00:00"}