{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EAEIVLBHGSDDNEHYXETK3WILMP","short_pith_number":"pith:EAEIVLBH","canonical_record":{"source":{"id":"1702.03303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-02-10T19:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"780238eddeca192e2b759bbe0af0b565366bd350b7f3f189cf80b8dc5743e94a","abstract_canon_sha256":"cb7c1bff75fee62466f1b46fc7ec305ddd4f3eb256b30fa0c8c54053fabd6520"},"schema_version":"1.0"},"canonical_sha256":"20088aac2734863690f8b926add90b63effe7d7e1d0eb3000bee340f1fcb7213","source":{"kind":"arxiv","id":"1702.03303","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03303","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03303v2","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03303","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"EAEIVLBHGSDD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EAEIVLBHGSDDNEHY","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EAEIVLBH","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EAEIVLBHGSDDNEHYXETK3WILMP","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-02-10T19:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"780238eddeca192e2b759bbe0af0b565366bd350b7f3f189cf80b8dc5743e94a","abstract_canon_sha256":"cb7c1bff75fee62466f1b46fc7ec305ddd4f3eb256b30fa0c8c54053fabd6520"},"schema_version":"1.0"},"canonical_sha256":"20088aac2734863690f8b926add90b63effe7d7e1d0eb3000bee340f1fcb7213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:39.966173Z","signature_b64":"3qeiFYLSnawSLhKdxbi+LazYN4ENJM6VqL5+iLTokdKg3pFqV873H7sAEir8Xph/kE/u1XqagcyRzUYoD16LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20088aac2734863690f8b926add90b63effe7d7e1d0eb3000bee340f1fcb7213","last_reissued_at":"2026-05-18T00:20:39.965542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:39.965542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03303","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4xUSjxDRTyN1qAoKbsFFW8MJF6LqQPIrZs714riZ8t9EjgMfmKvIb4xrMpSrFPDcKP6thk8KCqYvbtSLMfDQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:09.170364Z"},"content_sha256":"8e5c36ec340e2f2c9b80bd7bcc931439472ba1e7c8e5dcea0afb51b79fecd9c9","schema_version":"1.0","event_id":"sha256:8e5c36ec340e2f2c9b80bd7bcc931439472ba1e7c8e5dcea0afb51b79fecd9c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EAEIVLBHGSDDNEHYXETK3WILMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general limit lifting theorem for 2-dimensional monad theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Martin Szyld","submitted_at":"2017-02-10T19:02:57Z","abstract_excerpt":"We give a definition of weak morphism of $T$-algebras, for a $2$-monad $T$, with respect to an arbitrary family $\\Omega$ of $2$-cells of the base $2$-category. By considering particular choices of $\\Omega$, we recover the concepts of lax, pseudo and strict morphisms of $T$-algebras. We give a general notion of weak limit, and define what it means for such a limit to be compatible with another family of $2$-cells. These concepts allow us to prove a limit lifting theorem which unifies and generalizes three different previously known results of $2$-dimensional monad theory. Explicitly, by conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03303","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KPfp2k9pKFOkUbKapO4j7kcixtAuVCmW38BjFe6MufU0GDG/bWnVhvi/ckKRLhirLIV/3nNaEgUZ9/fVbI+QDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:09.170722Z"},"content_sha256":"df635c60b09dbf0228bf312b894659a08a06d118f03ecb464319a4289bb32bc0","schema_version":"1.0","event_id":"sha256:df635c60b09dbf0228bf312b894659a08a06d118f03ecb464319a4289bb32bc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EAEIVLBHGSDDNEHYXETK3WILMP/bundle.json","state_url":"https://pith.science/pith/EAEIVLBHGSDDNEHYXETK3WILMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EAEIVLBHGSDDNEHYXETK3WILMP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T19:11:09Z","links":{"resolver":"https://pith.science/pith/EAEIVLBHGSDDNEHYXETK3WILMP","bundle":"https://pith.science/pith/EAEIVLBHGSDDNEHYXETK3WILMP/bundle.json","state":"https://pith.science/pith/EAEIVLBHGSDDNEHYXETK3WILMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EAEIVLBHGSDDNEHYXETK3WILMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EAEIVLBHGSDDNEHYXETK3WILMP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cb7c1bff75fee62466f1b46fc7ec305ddd4f3eb256b30fa0c8c54053fabd6520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-02-10T19:02:57Z","title_canon_sha256":"780238eddeca192e2b759bbe0af0b565366bd350b7f3f189cf80b8dc5743e94a"},"schema_version":"1.0","source":{"id":"1702.03303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03303","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03303v2","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03303","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"EAEIVLBHGSDD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EAEIVLBHGSDDNEHY","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EAEIVLBH","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:df635c60b09dbf0228bf312b894659a08a06d118f03ecb464319a4289bb32bc0","target":"graph","created_at":"2026-05-18T00:20:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a definition of weak morphism of $T$-algebras, for a $2$-monad $T$, with respect to an arbitrary family $\\Omega$ of $2$-cells of the base $2$-category. By considering particular choices of $\\Omega$, we recover the concepts of lax, pseudo and strict morphisms of $T$-algebras. We give a general notion of weak limit, and define what it means for such a limit to be compatible with another family of $2$-cells. These concepts allow us to prove a limit lifting theorem which unifies and generalizes three different previously known results of $2$-dimensional monad theory. Explicitly, by conside","authors_text":"Martin Szyld","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-02-10T19:02:57Z","title":"A general limit lifting theorem for 2-dimensional monad theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03303","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8e5c36ec340e2f2c9b80bd7bcc931439472ba1e7c8e5dcea0afb51b79fecd9c9","target":"record","created_at":"2026-05-18T00:20:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cb7c1bff75fee62466f1b46fc7ec305ddd4f3eb256b30fa0c8c54053fabd6520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-02-10T19:02:57Z","title_canon_sha256":"780238eddeca192e2b759bbe0af0b565366bd350b7f3f189cf80b8dc5743e94a"},"schema_version":"1.0","source":{"id":"1702.03303","kind":"arxiv","version":2}},"canonical_sha256":"20088aac2734863690f8b926add90b63effe7d7e1d0eb3000bee340f1fcb7213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20088aac2734863690f8b926add90b63effe7d7e1d0eb3000bee340f1fcb7213","first_computed_at":"2026-05-18T00:20:39.965542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:39.965542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qeiFYLSnawSLhKdxbi+LazYN4ENJM6VqL5+iLTokdKg3pFqV873H7sAEir8Xph/kE/u1XqagcyRzUYoD16LDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:39.966173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e5c36ec340e2f2c9b80bd7bcc931439472ba1e7c8e5dcea0afb51b79fecd9c9","sha256:df635c60b09dbf0228bf312b894659a08a06d118f03ecb464319a4289bb32bc0"],"state_sha256":"cf5f837aaf4809ffec4d2f4401112c7269d618e045ce3f7b52f3bf8e144e2e97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/BqxLMFbQ2BGFQI1NfxwTSj2JGbXP0v2R1Fhv/PWMKw4iUdsUxHT0ns4N27Nrr158uO/LYgk5de0g9L9WO9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:11:09.172818Z","bundle_sha256":"cabc23890bfdb1ec8607e17ee2b2ca845f18afa9015683c9e0e6f29497721617"}}