{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Y2LGY6B2ULFK3EG33P7BD273Z2","short_pith_number":"pith:Y2LGY6B2","schema_version":"1.0","canonical_sha256":"c6966c783aa2caad90dbdbfe11ebfbce941a4ac90668e20629b9d1a3750ab23f","source":{"kind":"arxiv","id":"1503.06469","version":2},"attestation_state":"computed","paper":{"title":"Lax orthogonal factorisation systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Ignacio Lopez Franco, Maria Manuel Clementino","submitted_at":"2015-03-22T19:39:44Z","abstract_excerpt":"This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studi"},"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":"1503.06469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-22T19:39:44Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f0e2135d52c2f018f0977967d4e8bb25118ec48fd8b7be8b458f99964c00caa0","abstract_canon_sha256":"f601e0c9ae68f9725023d7288f798e138d547c107775dc4a040c2e2b314fa40c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:50.639077Z","signature_b64":"tdjc/lWeEZ0y/pyCWv96VDDtJXwGcZTFJw/4MNUeu4azCPGeYkxcfsUDm/QDj2s8tc9LAmimp3F42eEYcTAQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6966c783aa2caad90dbdbfe11ebfbce941a4ac90668e20629b9d1a3750ab23f","last_reissued_at":"2026-05-18T01:04:50.638600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:50.638600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lax orthogonal factorisation systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Ignacio Lopez Franco, Maria Manuel Clementino","submitted_at":"2015-03-22T19:39:44Z","abstract_excerpt":"This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06469","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":"1503.06469","created_at":"2026-05-18T01:04:50.638689+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06469v2","created_at":"2026-05-18T01:04:50.638689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06469","created_at":"2026-05-18T01:04:50.638689+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2LGY6B2ULFK","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2LGY6B2ULFK3EG3","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2LGY6B2","created_at":"2026-05-18T12:29:50.041715+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/Y2LGY6B2ULFK3EG33P7BD273Z2","json":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2.json","graph_json":"https://pith.science/api/pith-number/Y2LGY6B2ULFK3EG33P7BD273Z2/graph.json","events_json":"https://pith.science/api/pith-number/Y2LGY6B2ULFK3EG33P7BD273Z2/events.json","paper":"https://pith.science/paper/Y2LGY6B2"},"agent_actions":{"view_html":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2","download_json":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2.json","view_paper":"https://pith.science/paper/Y2LGY6B2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06469&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2LGY6B2ULFK3EG33P7BD273Z2/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2LGY6B2ULFK3EG33P7BD273Z2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2/action/storage_attestation","attest_author":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2/action/author_attestation","sign_citation":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2/action/citation_signature","submit_replication":"https://pith.science/pith/Y2LGY6B2ULFK3EG33P7BD273Z2/action/replication_record"}},"created_at":"2026-05-18T01:04:50.638689+00:00","updated_at":"2026-05-18T01:04:50.638689+00:00"}