{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DPUKNCW2SALMZEXNOUYTGAR6ND","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":"bb5325f7c7c142f945d20a15da2e92d2d3d1ace4818524886b89a2a3b5022fea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-10-18T15:28:03Z","title_canon_sha256":"b7aecba83d0ed24afadd1115d003abb648d4e2a7f20059108576e01ec6098176"},"schema_version":"1.0","source":{"id":"1010.3628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3628","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3628v2","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3628","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"DPUKNCW2SALM","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DPUKNCW2SALMZEXN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DPUKNCW2","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ff70f74802e2a43d8020efc010bee3ab0c59b956918e6675eb2c12fc43dc61fe","target":"graph","created_at":"2026-05-18T04:24:07Z","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":"For a generalisation of the classical theory of Hopf algebra over fields, A. Brugui\\`eres and A. Virelizier study opmonoidal monads on monoidal categories (which they called {\\em bimonads}). In a recent joint paper with S. Lack the same authors define the notion of a {\\em pre-Hopf monad} by requiring only a special form of the fusion operator to be invertible. In previous papers it was observed by the present authors that bimonads yield a special case %Hopf monads may be considered as a special case of an entwining of a pair of functors (on arbitrary categories). The purpose of this note is to","authors_text":"Bachuki Mesablishvili, Robert Wisbauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-10-18T15:28:03Z","title":"Notes on bimonads and Hopf monads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3628","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:c9e80301d0206538eef28176b743aefe78678b1649961fb164cd8bb49f74a9d8","target":"record","created_at":"2026-05-18T04:24:07Z","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":"bb5325f7c7c142f945d20a15da2e92d2d3d1ace4818524886b89a2a3b5022fea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-10-18T15:28:03Z","title_canon_sha256":"b7aecba83d0ed24afadd1115d003abb648d4e2a7f20059108576e01ec6098176"},"schema_version":"1.0","source":{"id":"1010.3628","kind":"arxiv","version":2}},"canonical_sha256":"1be8a68ada9016cc92ed753133023e68d8d294692dfedaac78a10f52eae12c86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be8a68ada9016cc92ed753133023e68d8d294692dfedaac78a10f52eae12c86","first_computed_at":"2026-05-18T04:24:07.156075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:07.156075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2lHsMZ1mIfB6ZZaFEAoYIgg7FD1f2xVhDzKseIubPPEhFXakNWHAx+X4+IfFQKg4HHoAs53yiImm/uJnMwZiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:07.156700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e80301d0206538eef28176b743aefe78678b1649961fb164cd8bb49f74a9d8","sha256:ff70f74802e2a43d8020efc010bee3ab0c59b956918e6675eb2c12fc43dc61fe"],"state_sha256":"581e3c6de213efcd6f3110de742b867becb5cc85eed38619be08bb956450fa37"}