{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WJLLJWTMZ4VKI3U7IRM6SBFQAU","short_pith_number":"pith:WJLLJWTM","schema_version":"1.0","canonical_sha256":"b256b4da6ccf2aa46e9f4459e904b0050179c7f332848d0a2bcfe9ca2a88a2bb","source":{"kind":"arxiv","id":"1909.13564","version":2},"attestation_state":"computed","paper":{"title":"The folk model category structure on strict $\\omega$-categories is monoidal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Dimitri Ara, Maxime Lucas","submitted_at":"2019-09-30T10:05:41Z","abstract_excerpt":"We prove that the folk model category structure on the category of strict $\\omega$-categories, introduced by Lafont, M\\'etayer and Worytkiewicz, is monoidal, first, for the Gray tensor product and, second, for the join of $\\omega$-categories, introduced by the first author and Maltsiniotis. We moreover show that the Gray tensor product induces, by adjunction, a tensor product of strict $(m,n)$-categories and that this tensor product is also compatible with the folk model category structure. In particular, we get a monoidal model category structure on the category of strict $\\omega$-groupoids. "},"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":"1909.13564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-09-30T10:05:41Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a9dc425846db918b68ab171e142ca99b08bc7afd72e5c5235d790f6bb7422ada","abstract_canon_sha256":"e5469e02e7d9033279dfa7d58c649aea62a234296504b756475d74ca0764e2fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:32:56.709665Z","signature_b64":"BEXwgEEttvEt0sRFGerZ3RZcLNZHKQTTXq/KUk5yu3plG+yjTRWpQven6hUybW4o4phM3ZJ8knnIN25hWQT1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b256b4da6ccf2aa46e9f4459e904b0050179c7f332848d0a2bcfe9ca2a88a2bb","last_reissued_at":"2026-07-05T01:32:56.709292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:32:56.709292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The folk model category structure on strict $\\omega$-categories is monoidal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Dimitri Ara, Maxime Lucas","submitted_at":"2019-09-30T10:05:41Z","abstract_excerpt":"We prove that the folk model category structure on the category of strict $\\omega$-categories, introduced by Lafont, M\\'etayer and Worytkiewicz, is monoidal, first, for the Gray tensor product and, second, for the join of $\\omega$-categories, introduced by the first author and Maltsiniotis. We moreover show that the Gray tensor product induces, by adjunction, a tensor product of strict $(m,n)$-categories and that this tensor product is also compatible with the folk model category structure. In particular, we get a monoidal model category structure on the category of strict $\\omega$-groupoids. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13564","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.13564/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.13564","created_at":"2026-07-05T01:32:56.709370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.13564v2","created_at":"2026-07-05T01:32:56.709370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13564","created_at":"2026-07-05T01:32:56.709370+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJLLJWTMZ4VK","created_at":"2026-07-05T01:32:56.709370+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJLLJWTMZ4VKI3U7","created_at":"2026-07-05T01:32:56.709370+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJLLJWTM","created_at":"2026-07-05T01:32:56.709370+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07431","citing_title":"Higher Semiadditive Character Theory","ref_index":69,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU","json":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU.json","graph_json":"https://pith.science/api/pith-number/WJLLJWTMZ4VKI3U7IRM6SBFQAU/graph.json","events_json":"https://pith.science/api/pith-number/WJLLJWTMZ4VKI3U7IRM6SBFQAU/events.json","paper":"https://pith.science/paper/WJLLJWTM"},"agent_actions":{"view_html":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU","download_json":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU.json","view_paper":"https://pith.science/paper/WJLLJWTM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.13564&json=true","fetch_graph":"https://pith.science/api/pith-number/WJLLJWTMZ4VKI3U7IRM6SBFQAU/graph.json","fetch_events":"https://pith.science/api/pith-number/WJLLJWTMZ4VKI3U7IRM6SBFQAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU/action/storage_attestation","attest_author":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU/action/author_attestation","sign_citation":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU/action/citation_signature","submit_replication":"https://pith.science/pith/WJLLJWTMZ4VKI3U7IRM6SBFQAU/action/replication_record"}},"created_at":"2026-07-05T01:32:56.709370+00:00","updated_at":"2026-07-05T01:32:56.709370+00:00"}