{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6TXQUEM6CH4W6WUGJFYKQJUPRZ","short_pith_number":"pith:6TXQUEM6","schema_version":"1.0","canonical_sha256":"f4ef0a119e11f96f5a864970a8268f8e477c3e1b54990e480c5de6150238d47b","source":{"kind":"arxiv","id":"1303.3070","version":2},"attestation_state":"computed","paper":{"title":"Transparency condition in the categories of Yetter-Drinfel'd modules over Hopf algebras in braided categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bojana Femi\\'c","submitted_at":"2013-03-13T00:45:59Z","abstract_excerpt":"We study versions of the categories of Yetter-Drinfel'd modules over a Hopf algebra $H$ in a braided monoidal category $\\C$. Contrarywise to Bespalov's approach, all our structures live in $\\C$. This forces $H$ to be transparent or equivalently to lie in M\\\"uger's center $\\Z_2(\\C)$ of $\\C$. We prove that versions of the categories of Yetter-Drinfel'd modules in $\\C$ are braided monoidally isomorphic to the categories of (left/right) modules over the Drinfel'd double $D(H)\\in\\C$ for $H$ finite. We obtain that these categories polarize into two disjoint groups of mutually isomorphic braided mono"},"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":"1303.3070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-13T00:45:59Z","cross_cats_sorted":[],"title_canon_sha256":"1542a08b3e9c97b39988db1081e95856f72dd1228d0e6346656090f17474a92c","abstract_canon_sha256":"1bf51d65116e6b2e7b075151a9d9c703687f51fcde8b7754b69b0ef00e15b7a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:34.355141Z","signature_b64":"vmt1jZbgJ04pPI91tqAGDB1QIWMsYPrVtgu2vdM1OYdnkXO/FkGoByfYHubmmjAU8pCsgvHh4IreKUEiIaY7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ef0a119e11f96f5a864970a8268f8e477c3e1b54990e480c5de6150238d47b","last_reissued_at":"2026-05-18T03:07:34.354521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:34.354521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transparency condition in the categories of Yetter-Drinfel'd modules over Hopf algebras in braided categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bojana Femi\\'c","submitted_at":"2013-03-13T00:45:59Z","abstract_excerpt":"We study versions of the categories of Yetter-Drinfel'd modules over a Hopf algebra $H$ in a braided monoidal category $\\C$. Contrarywise to Bespalov's approach, all our structures live in $\\C$. This forces $H$ to be transparent or equivalently to lie in M\\\"uger's center $\\Z_2(\\C)$ of $\\C$. We prove that versions of the categories of Yetter-Drinfel'd modules in $\\C$ are braided monoidally isomorphic to the categories of (left/right) modules over the Drinfel'd double $D(H)\\in\\C$ for $H$ finite. We obtain that these categories polarize into two disjoint groups of mutually isomorphic braided mono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3070","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":"1303.3070","created_at":"2026-05-18T03:07:34.354618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3070v2","created_at":"2026-05-18T03:07:34.354618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3070","created_at":"2026-05-18T03:07:34.354618+00:00"},{"alias_kind":"pith_short_12","alias_value":"6TXQUEM6CH4W","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6TXQUEM6CH4W6WUG","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6TXQUEM6","created_at":"2026-05-18T12:27:36.564083+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/6TXQUEM6CH4W6WUGJFYKQJUPRZ","json":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ.json","graph_json":"https://pith.science/api/pith-number/6TXQUEM6CH4W6WUGJFYKQJUPRZ/graph.json","events_json":"https://pith.science/api/pith-number/6TXQUEM6CH4W6WUGJFYKQJUPRZ/events.json","paper":"https://pith.science/paper/6TXQUEM6"},"agent_actions":{"view_html":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ","download_json":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ.json","view_paper":"https://pith.science/paper/6TXQUEM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3070&json=true","fetch_graph":"https://pith.science/api/pith-number/6TXQUEM6CH4W6WUGJFYKQJUPRZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6TXQUEM6CH4W6WUGJFYKQJUPRZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ/action/storage_attestation","attest_author":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ/action/author_attestation","sign_citation":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ/action/citation_signature","submit_replication":"https://pith.science/pith/6TXQUEM6CH4W6WUGJFYKQJUPRZ/action/replication_record"}},"created_at":"2026-05-18T03:07:34.354618+00:00","updated_at":"2026-05-18T03:07:34.354618+00:00"}