{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GFRAJ7APZ3UA4QBIAVW7VC7VR6","short_pith_number":"pith:GFRAJ7AP","schema_version":"1.0","canonical_sha256":"316204fc0fcee80e4028056dfa8bf58f983412375f6f7e7ec1ac5419d0d2952b","source":{"kind":"arxiv","id":"1208.5693","version":1},"attestation_state":"computed","paper":{"title":"The doubles of a braided Hopf algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alain Brugui\\`eres, Alexis Virelizier","submitted_at":"2012-08-28T15:48:54Z","abstract_excerpt":"Let A be a Hopf algebra in a braided rigid category B. In the case B admits a coend C, which is a Hopf algebra in B, we defined in 2008 the double D(A) of A, which is a quasitriangular Hopf algebra in B whose category of modules is isomorphic to the center of the category of A-modules as a braided category. Here, quasitriangular means endowed with an R-matrix (our notion of R-matrix for a Hopf algebra in B involves the coend C of B). In general, i.e. when B does not necessarily admit a coend, we construct a quasitriangular Hopf monad d_A on the center Z(B) of B whose category of modules is iso"},"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":"1208.5693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-08-28T15:48:54Z","cross_cats_sorted":[],"title_canon_sha256":"5305c847b9a00b2f87bafa4d707018bd5d565491d312867ba5efa212181fccf7","abstract_canon_sha256":"8f7f28493ee5c5806cf84158b7ac54f7ab7013e7dc71846b20a6d7c1dd7c2870"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:58.002707Z","signature_b64":"Wcv/ft7jhv8ML3SvUYAJKY/qqeAs29i4SjxvbW28RBNQl1ee9YcuUB8IN9OuekB8MPAh//DmqF3AXYLzghYSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"316204fc0fcee80e4028056dfa8bf58f983412375f6f7e7ec1ac5419d0d2952b","last_reissued_at":"2026-05-18T03:46:58.001925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:58.001925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The doubles of a braided Hopf algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alain Brugui\\`eres, Alexis Virelizier","submitted_at":"2012-08-28T15:48:54Z","abstract_excerpt":"Let A be a Hopf algebra in a braided rigid category B. In the case B admits a coend C, which is a Hopf algebra in B, we defined in 2008 the double D(A) of A, which is a quasitriangular Hopf algebra in B whose category of modules is isomorphic to the center of the category of A-modules as a braided category. Here, quasitriangular means endowed with an R-matrix (our notion of R-matrix for a Hopf algebra in B involves the coend C of B). In general, i.e. when B does not necessarily admit a coend, we construct a quasitriangular Hopf monad d_A on the center Z(B) of B whose category of modules is iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5693","kind":"arxiv","version":1},"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":"1208.5693","created_at":"2026-05-18T03:46:58.002078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5693v1","created_at":"2026-05-18T03:46:58.002078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5693","created_at":"2026-05-18T03:46:58.002078+00:00"},{"alias_kind":"pith_short_12","alias_value":"GFRAJ7APZ3UA","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GFRAJ7APZ3UA4QBI","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GFRAJ7AP","created_at":"2026-05-18T12:27:06.952714+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/GFRAJ7APZ3UA4QBIAVW7VC7VR6","json":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6.json","graph_json":"https://pith.science/api/pith-number/GFRAJ7APZ3UA4QBIAVW7VC7VR6/graph.json","events_json":"https://pith.science/api/pith-number/GFRAJ7APZ3UA4QBIAVW7VC7VR6/events.json","paper":"https://pith.science/paper/GFRAJ7AP"},"agent_actions":{"view_html":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6","download_json":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6.json","view_paper":"https://pith.science/paper/GFRAJ7AP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5693&json=true","fetch_graph":"https://pith.science/api/pith-number/GFRAJ7APZ3UA4QBIAVW7VC7VR6/graph.json","fetch_events":"https://pith.science/api/pith-number/GFRAJ7APZ3UA4QBIAVW7VC7VR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6/action/storage_attestation","attest_author":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6/action/author_attestation","sign_citation":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6/action/citation_signature","submit_replication":"https://pith.science/pith/GFRAJ7APZ3UA4QBIAVW7VC7VR6/action/replication_record"}},"created_at":"2026-05-18T03:46:58.002078+00:00","updated_at":"2026-05-18T03:46:58.002078+00:00"}