{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2DCOBTI33LFDAWHESKMAGDSNMQ","short_pith_number":"pith:2DCOBTI3","schema_version":"1.0","canonical_sha256":"d0c4e0cd1bdaca3058e49298030e4d641bdaa2e3e55649504086ffc1024aa115","source":{"kind":"arxiv","id":"1306.4119","version":1},"attestation_state":"computed","paper":{"title":"Groupoids, Frobenius algebras and Poisson sigma models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"Ivan Contreras","submitted_at":"2013-06-18T09:29:12Z","abstract_excerpt":"In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius algebras in the category Rel, as well as an adjunction between a special type of semigroupoids and relative H*-algebras. The connection between groupoids and Frobenius algebras is made explicit by introducing what we called weak monoids and relational symplectic groupoids, in the context of Poisson sigma models with boundary and in particular, describing such struc"},"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":"1306.4119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-18T09:29:12Z","cross_cats_sorted":["math.CT","math.MP"],"title_canon_sha256":"c8460be26fc9ebc91f4eabaa1b7eb2f6b94f0616da175b0c4c49d60a11b27c94","abstract_canon_sha256":"3cad030b8ddb6bba56ab225f96776a78fee129e39eb029e0c7f29e93a54f4a95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:24.586370Z","signature_b64":"jdCk2W+nOuucwvkN2KqAAIRpU2In9NNDyy0V9mGEGiARjzOIleoBd2ntd8k7W+tMD2LGf5JBvnctwsg5XtHIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0c4e0cd1bdaca3058e49298030e4d641bdaa2e3e55649504086ffc1024aa115","last_reissued_at":"2026-05-18T01:33:24.585681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:24.585681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groupoids, Frobenius algebras and Poisson sigma models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"Ivan Contreras","submitted_at":"2013-06-18T09:29:12Z","abstract_excerpt":"In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius algebras in the category Rel, as well as an adjunction between a special type of semigroupoids and relative H*-algebras. The connection between groupoids and Frobenius algebras is made explicit by introducing what we called weak monoids and relational symplectic groupoids, in the context of Poisson sigma models with boundary and in particular, describing such struc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4119","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":"1306.4119","created_at":"2026-05-18T01:33:24.585790+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.4119v1","created_at":"2026-05-18T01:33:24.585790+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4119","created_at":"2026-05-18T01:33:24.585790+00:00"},{"alias_kind":"pith_short_12","alias_value":"2DCOBTI33LFD","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"2DCOBTI33LFDAWHE","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"2DCOBTI3","created_at":"2026-05-18T12:27:30.460161+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/2DCOBTI33LFDAWHESKMAGDSNMQ","json":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ.json","graph_json":"https://pith.science/api/pith-number/2DCOBTI33LFDAWHESKMAGDSNMQ/graph.json","events_json":"https://pith.science/api/pith-number/2DCOBTI33LFDAWHESKMAGDSNMQ/events.json","paper":"https://pith.science/paper/2DCOBTI3"},"agent_actions":{"view_html":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ","download_json":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ.json","view_paper":"https://pith.science/paper/2DCOBTI3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.4119&json=true","fetch_graph":"https://pith.science/api/pith-number/2DCOBTI33LFDAWHESKMAGDSNMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2DCOBTI33LFDAWHESKMAGDSNMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ/action/storage_attestation","attest_author":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ/action/author_attestation","sign_citation":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ/action/citation_signature","submit_replication":"https://pith.science/pith/2DCOBTI33LFDAWHESKMAGDSNMQ/action/replication_record"}},"created_at":"2026-05-18T01:33:24.585790+00:00","updated_at":"2026-05-18T01:33:24.585790+00:00"}