{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GTPEUTFAPSFMMPAWALBZOBSDXI","short_pith_number":"pith:GTPEUTFA","schema_version":"1.0","canonical_sha256":"34de4a4ca07c8ac63c1602c3970643ba3643f4d54b0fca64225ffa41c7809f51","source":{"kind":"arxiv","id":"1511.03806","version":2},"attestation_state":"computed","paper":{"title":"Multiplier Hopf monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Gabriella B\"ohm, Stephen Lack","submitted_at":"2015-11-12T07:53:34Z","abstract_excerpt":"The notion of multiplier Hopf monoid in any braided monoidal category is introduced as a multiplier bimonoid whose constituent fusion morphisms are isomorphisms. In the category of vector spaces over the complex numbers, Van Daele's definition of multiplier Hopf algebra is re-obtained. It is shown that the key features of multiplier Hopf algebras (over fields) remain valid in this more general context. Namely, for a multiplier Hopf monoid A, the existence of a unique antipode is proved --- in an appropriate, multiplier-valued sense --- which is shown to be a morphism of multiplier bimonoids fr"},"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":"1511.03806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-11-12T07:53:34Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"bf74221bc0f7bbf1f38bf73fc0a899aa86a1d1843a49cbd3635dced19384a806","abstract_canon_sha256":"f8184bb9fbfd9a0b2e63e6b5bc2318f4b0751eea5aa86f7acb3d19312a41cd4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.125606Z","signature_b64":"tmFHEqz1HZbyZ12dg3U9n/UTwod25xmTql0CdOX3KkU1lqu9oCvayen/QBA2spFYSJaBC+LwlpZWV7uX3PkUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34de4a4ca07c8ac63c1602c3970643ba3643f4d54b0fca64225ffa41c7809f51","last_reissued_at":"2026-05-17T23:41:28.124807Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.124807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplier Hopf monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Gabriella B\"ohm, Stephen Lack","submitted_at":"2015-11-12T07:53:34Z","abstract_excerpt":"The notion of multiplier Hopf monoid in any braided monoidal category is introduced as a multiplier bimonoid whose constituent fusion morphisms are isomorphisms. In the category of vector spaces over the complex numbers, Van Daele's definition of multiplier Hopf algebra is re-obtained. It is shown that the key features of multiplier Hopf algebras (over fields) remain valid in this more general context. Namely, for a multiplier Hopf monoid A, the existence of a unique antipode is proved --- in an appropriate, multiplier-valued sense --- which is shown to be a morphism of multiplier bimonoids fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03806","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":"1511.03806","created_at":"2026-05-17T23:41:28.124933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03806v2","created_at":"2026-05-17T23:41:28.124933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03806","created_at":"2026-05-17T23:41:28.124933+00:00"},{"alias_kind":"pith_short_12","alias_value":"GTPEUTFAPSFM","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GTPEUTFAPSFMMPAW","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GTPEUTFA","created_at":"2026-05-18T12:29:22.688609+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/GTPEUTFAPSFMMPAWALBZOBSDXI","json":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI.json","graph_json":"https://pith.science/api/pith-number/GTPEUTFAPSFMMPAWALBZOBSDXI/graph.json","events_json":"https://pith.science/api/pith-number/GTPEUTFAPSFMMPAWALBZOBSDXI/events.json","paper":"https://pith.science/paper/GTPEUTFA"},"agent_actions":{"view_html":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI","download_json":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI.json","view_paper":"https://pith.science/paper/GTPEUTFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03806&json=true","fetch_graph":"https://pith.science/api/pith-number/GTPEUTFAPSFMMPAWALBZOBSDXI/graph.json","fetch_events":"https://pith.science/api/pith-number/GTPEUTFAPSFMMPAWALBZOBSDXI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI/action/storage_attestation","attest_author":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI/action/author_attestation","sign_citation":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI/action/citation_signature","submit_replication":"https://pith.science/pith/GTPEUTFAPSFMMPAWALBZOBSDXI/action/replication_record"}},"created_at":"2026-05-17T23:41:28.124933+00:00","updated_at":"2026-05-17T23:41:28.124933+00:00"}