{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:2N2MLYCXYP6RC3PHA3AJNWZ572","short_pith_number":"pith:2N2MLYCX","schema_version":"1.0","canonical_sha256":"d374c5e057c3fd116de706c096db3dfe9ea2279fbd91ae06cefad2d9cca0681e","source":{"kind":"arxiv","id":"math/0106050","version":4},"attestation_state":"computed","paper":{"title":"Category theory for conformal boundary conditions","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.CT","authors_text":"C. Schweigert, J. Fuchs","submitted_at":"2001-06-07T18:34:04Z","abstract_excerpt":"We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity.\n  We apply our results to the description of boundary conditions in two-dimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives r"},"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":"math/0106050","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2001-06-07T18:34:04Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"8f3d44fbb79914dc55f48fe00ec0bd35c8672fda631bf882d5b9601f7914b02f","abstract_canon_sha256":"5c47b4b8537dd3e22a276607280fef3532c04e0cda24c17e39d86e4613563906"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:49:40.775004Z","signature_b64":"d8m7DcSw/uS0NqyzZSAoH6yRexKR6jiFXyq3LPAgHQlhroGSjESr84XXtJ1YIjXbuAEkOB8Vpj+ku1g5hjCTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d374c5e057c3fd116de706c096db3dfe9ea2279fbd91ae06cefad2d9cca0681e","last_reissued_at":"2026-07-04T14:49:40.774606Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:49:40.774606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Category theory for conformal boundary conditions","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.CT","authors_text":"C. Schweigert, J. Fuchs","submitted_at":"2001-06-07T18:34:04Z","abstract_excerpt":"We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity.\n  We apply our results to the description of boundary conditions in two-dimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106050","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0106050/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0106050","created_at":"2026-07-04T14:49:40.774662+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0106050v4","created_at":"2026-07-04T14:49:40.774662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106050","created_at":"2026-07-04T14:49:40.774662+00:00"},{"alias_kind":"pith_short_12","alias_value":"2N2MLYCXYP6R","created_at":"2026-07-04T14:49:40.774662+00:00"},{"alias_kind":"pith_short_16","alias_value":"2N2MLYCXYP6RC3PH","created_at":"2026-07-04T14:49:40.774662+00:00"},{"alias_kind":"pith_short_8","alias_value":"2N2MLYCX","created_at":"2026-07-04T14:49:40.774662+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":185,"is_internal_anchor":true},{"citing_arxiv_id":"2605.24978","citing_title":"Defect Conformal Manifolds along RG Domain Walls between $\\mathbb Z_N$-Parafermions and Minimal Models","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":191,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572","json":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572.json","graph_json":"https://pith.science/api/pith-number/2N2MLYCXYP6RC3PHA3AJNWZ572/graph.json","events_json":"https://pith.science/api/pith-number/2N2MLYCXYP6RC3PHA3AJNWZ572/events.json","paper":"https://pith.science/paper/2N2MLYCX"},"agent_actions":{"view_html":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572","download_json":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572.json","view_paper":"https://pith.science/paper/2N2MLYCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0106050&json=true","fetch_graph":"https://pith.science/api/pith-number/2N2MLYCXYP6RC3PHA3AJNWZ572/graph.json","fetch_events":"https://pith.science/api/pith-number/2N2MLYCXYP6RC3PHA3AJNWZ572/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572/action/storage_attestation","attest_author":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572/action/author_attestation","sign_citation":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572/action/citation_signature","submit_replication":"https://pith.science/pith/2N2MLYCXYP6RC3PHA3AJNWZ572/action/replication_record"}},"created_at":"2026-07-04T14:49:40.774662+00:00","updated_at":"2026-07-04T14:49:40.774662+00:00"}