{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y5YASGCJJ4JS2XJLICJID7VZGH","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":"cdcca60923161db7034c1845b225071eb8d3df7e4d0f50a30cd87b988bd2b3d7","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-28T16:15:39Z","title_canon_sha256":"65fd3de7c95d9c87ebcf7bb34dd45075f5f599f15ea69510974e12487817be76"},"schema_version":"1.0","source":{"id":"1407.7461","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7461","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7461v3","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7461","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"Y5YASGCJJ4JS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y5YASGCJJ4JS2XJL","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y5YASGCJ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:a8912de3bd2e3abb47d5ab76b53a78c6dc557d47ebe6cae04cc205d7cb54dd2f","target":"graph","created_at":"2026-05-18T00:50:57Z","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 show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting them. This gives a positive answer to a conjecture due to Hovey and Strickland. We also prove that principal (left) bundles lead to a bicategory together with a 2-functor from flat Hopf algebroids to trivial principal bundles. This turns out to be the universal solution for 2-functors which send weak equivalences to invertible 1-cells. Our approach can be seen as an algebraic counterpart to Lie groupoid Morita theory.","authors_text":"Laiachi El Kaoutit, Niels Kowalzig","cross_cats":["math.AC","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-28T16:15:39Z","title":"Morita theory for Hopf algebroids, principal bibundles, and weak equivalences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7461","kind":"arxiv","version":3},"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:ac579b4e2ce825ce49c896ca79d8060359db8e08123214a9ab777adfb42211bf","target":"record","created_at":"2026-05-18T00:50:57Z","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":"cdcca60923161db7034c1845b225071eb8d3df7e4d0f50a30cd87b988bd2b3d7","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-28T16:15:39Z","title_canon_sha256":"65fd3de7c95d9c87ebcf7bb34dd45075f5f599f15ea69510974e12487817be76"},"schema_version":"1.0","source":{"id":"1407.7461","kind":"arxiv","version":3}},"canonical_sha256":"c7700918494f132d5d2b409281feb931d1c44f9f768f509830108c74421238dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7700918494f132d5d2b409281feb931d1c44f9f768f509830108c74421238dc","first_computed_at":"2026-05-18T00:50:57.984990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:57.984990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r1g78WSSkMjqR+vOP4u3rW0XnVfjB3hH23tQsEBfwgRWREDlcFBHX+utsyBVM+Rb3ZxnIl5zGjYkDiXZuYTZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:57.985594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7461","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac579b4e2ce825ce49c896ca79d8060359db8e08123214a9ab777adfb42211bf","sha256:a8912de3bd2e3abb47d5ab76b53a78c6dc557d47ebe6cae04cc205d7cb54dd2f"],"state_sha256":"a56d173fa4e9a6c85b722e78b2193a56fb97127f8af5cabed7174473d18e0cce"}