{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z56V3ROTYCNEZWAWY6XK57XPJR","short_pith_number":"pith:Z56V3ROT","canonical_record":{"source":{"id":"1104.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-04-12T04:37:07Z","cross_cats_sorted":[],"title_canon_sha256":"829db5c55f9b5c16e5faca809054d38cd1be23de1ef2f6c2ea6caf932b105c98","abstract_canon_sha256":"a814089f69951d300b9cf8895bfcee78c65b9d34fc7cfb860fcc985431f5f386"},"schema_version":"1.0"},"canonical_sha256":"cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4","source":{"kind":"arxiv","id":"1104.2111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2111","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2111v2","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2111","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z56V3ROTYCNE","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z56V3ROTYCNEZWAW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z56V3ROT","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z56V3ROTYCNEZWAWY6XK57XPJR","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-04-12T04:37:07Z","cross_cats_sorted":[],"title_canon_sha256":"829db5c55f9b5c16e5faca809054d38cd1be23de1ef2f6c2ea6caf932b105c98","abstract_canon_sha256":"a814089f69951d300b9cf8895bfcee78c65b9d34fc7cfb860fcc985431f5f386"},"schema_version":"1.0"},"canonical_sha256":"cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:11.982687Z","signature_b64":"EIksTfAuVB7pDjjBQBvtu2xqXkLPPjqe4u72o1THq4BfvoC10DugiLb+ddhK9x0cYV49XBMIq9mI4yY1QdC9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4","last_reissued_at":"2026-05-18T04:02:11.982006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:11.982006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2111","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":"2026-05-18T04:02:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MPJ4DAIhtfsk/MJiAM8pwyoWWiUBPjiIxO0+588qBKQq03fLCrHAlB7fxmI2KADb/xaidv4iHubKKhkfWx0BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:46:34.563663Z"},"content_sha256":"e5aadf7e0a3215f26880d696b70728e684c74fd23f7d712b97f93a6e8662de50","schema_version":"1.0","event_id":"sha256:e5aadf7e0a3215f26880d696b70728e684c74fd23f7d712b97f93a6e8662de50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z56V3ROTYCNEZWAWY6XK57XPJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enhanced 2-categories and limits for lax morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Michael Shulman, Stephen Lack","submitted_at":"2011-04-12T04:37:07Z","abstract_excerpt":"We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is done using the framework of 2-monads. In order to characterize the limits which exist in this context, we need to consider also the functors which do strictly preserve the extra structure. We show how such a 2-category of weak morphisms which is \"enhanced\", by specifying which of these weak morphisms are actually strict, can be thought of as category enriched o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2111","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":"2026-05-18T04:02:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yczseZ/4cYHQrq1nNM9MMD207LRRgM0FgecntZs5eDIFaPBOrRILFusfseziZM/wzGXtLG+CL1H/HY2ji+xlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:46:34.564010Z"},"content_sha256":"8cbc7014107ed921b71d7258a163ea80d03f43a672cb62a77503883e547077d4","schema_version":"1.0","event_id":"sha256:8cbc7014107ed921b71d7258a163ea80d03f43a672cb62a77503883e547077d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/bundle.json","state_url":"https://pith.science/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/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":"2026-06-03T14:46:34Z","links":{"resolver":"https://pith.science/pith/Z56V3ROTYCNEZWAWY6XK57XPJR","bundle":"https://pith.science/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/bundle.json","state":"https://pith.science/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z56V3ROTYCNEZWAWY6XK57XPJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z56V3ROTYCNEZWAWY6XK57XPJR","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":"a814089f69951d300b9cf8895bfcee78c65b9d34fc7cfb860fcc985431f5f386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-04-12T04:37:07Z","title_canon_sha256":"829db5c55f9b5c16e5faca809054d38cd1be23de1ef2f6c2ea6caf932b105c98"},"schema_version":"1.0","source":{"id":"1104.2111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2111","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2111v2","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2111","created_at":"2026-05-18T04:02:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z56V3ROTYCNE","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z56V3ROTYCNEZWAW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z56V3ROT","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:8cbc7014107ed921b71d7258a163ea80d03f43a672cb62a77503883e547077d4","target":"graph","created_at":"2026-05-18T04:02:11Z","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 study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is done using the framework of 2-monads. In order to characterize the limits which exist in this context, we need to consider also the functors which do strictly preserve the extra structure. We show how such a 2-category of weak morphisms which is \"enhanced\", by specifying which of these weak morphisms are actually strict, can be thought of as category enriched o","authors_text":"Michael Shulman, Stephen Lack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-04-12T04:37:07Z","title":"Enhanced 2-categories and limits for lax morphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2111","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:e5aadf7e0a3215f26880d696b70728e684c74fd23f7d712b97f93a6e8662de50","target":"record","created_at":"2026-05-18T04:02:11Z","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":"a814089f69951d300b9cf8895bfcee78c65b9d34fc7cfb860fcc985431f5f386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-04-12T04:37:07Z","title_canon_sha256":"829db5c55f9b5c16e5faca809054d38cd1be23de1ef2f6c2ea6caf932b105c98"},"schema_version":"1.0","source":{"id":"1104.2111","kind":"arxiv","version":2}},"canonical_sha256":"cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4","first_computed_at":"2026-05-18T04:02:11.982006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:11.982006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EIksTfAuVB7pDjjBQBvtu2xqXkLPPjqe4u72o1THq4BfvoC10DugiLb+ddhK9x0cYV49XBMIq9mI4yY1QdC9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:11.982687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5aadf7e0a3215f26880d696b70728e684c74fd23f7d712b97f93a6e8662de50","sha256:8cbc7014107ed921b71d7258a163ea80d03f43a672cb62a77503883e547077d4"],"state_sha256":"845377f5d4bffec1072f9d2fdfa5af5a4d1b7a3505509c54925822629dcd1fc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+gSxv13iYRj8WjnIwZOLlTgZO59dfzSMpyV0n/3ucw1504cAWktR8SLbltxBPqrq39H9D83a7JV+s+vlsCbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:46:34.565940Z","bundle_sha256":"9e52087ea24102856c0e3fea4c735e69dc36533ba01437c460c6d694c0994802"}}