{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:RSVXZQNKB454Q7DMU2ATWALZJC","short_pith_number":"pith:RSVXZQNK","schema_version":"1.0","canonical_sha256":"8cab7cc1aa0f3bc87c6ca6813b01794899fa0ba55691627ba5f87d4096a77a46","source":{"kind":"arxiv","id":"0711.0324","version":2},"attestation_state":"computed","paper":{"title":"Tensor product for symmetric monoidal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Vincent Schmitt","submitted_at":"2007-11-02T15:06:52Z","abstract_excerpt":"We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural transformations. Our tensor product together with a suitable unit is part of a structure on SMC that is a 2-categorical version of the symmetric monoidal closed categories. This structure is surprisingly simple. In particular the arrows involved in the associativity and symmetry laws for the tensor and in the unit cancellation laws are 2-natural and satisfy c"},"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":"0711.0324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2007-11-02T15:06:52Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8d0ed2cbeee9c25208349098ce7fa4210c67a919949d5b8af5abae95097bb07a","abstract_canon_sha256":"3a6f6ba211e31f5717d99fc9340b1a6c7029a057df56f078e665cb45e4a9cef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:12:05.643665Z","signature_b64":"SZcKhBLsxE4oaHfAmyfMGsL3AwWbJQn9+XK5vl9lcp2AkOFYpu9SIW9SljvDwVGFnAnEWooebsFwczSRiCHtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cab7cc1aa0f3bc87c6ca6813b01794899fa0ba55691627ba5f87d4096a77a46","last_reissued_at":"2026-07-04T15:12:05.643297Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:12:05.643297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor product for symmetric monoidal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Vincent Schmitt","submitted_at":"2007-11-02T15:06:52Z","abstract_excerpt":"We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural transformations. Our tensor product together with a suitable unit is part of a structure on SMC that is a 2-categorical version of the symmetric monoidal closed categories. This structure is surprisingly simple. In particular the arrows involved in the associativity and symmetry laws for the tensor and in the unit cancellation laws are 2-natural and satisfy c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0324","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0711.0324/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":"0711.0324","created_at":"2026-07-04T15:12:05.643372+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.0324v2","created_at":"2026-07-04T15:12:05.643372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0324","created_at":"2026-07-04T15:12:05.643372+00:00"},{"alias_kind":"pith_short_12","alias_value":"RSVXZQNKB454","created_at":"2026-07-04T15:12:05.643372+00:00"},{"alias_kind":"pith_short_16","alias_value":"RSVXZQNKB454Q7DM","created_at":"2026-07-04T15:12:05.643372+00:00"},{"alias_kind":"pith_short_8","alias_value":"RSVXZQNK","created_at":"2026-07-04T15:12:05.643372+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/RSVXZQNKB454Q7DMU2ATWALZJC","json":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC.json","graph_json":"https://pith.science/api/pith-number/RSVXZQNKB454Q7DMU2ATWALZJC/graph.json","events_json":"https://pith.science/api/pith-number/RSVXZQNKB454Q7DMU2ATWALZJC/events.json","paper":"https://pith.science/paper/RSVXZQNK"},"agent_actions":{"view_html":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC","download_json":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC.json","view_paper":"https://pith.science/paper/RSVXZQNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.0324&json=true","fetch_graph":"https://pith.science/api/pith-number/RSVXZQNKB454Q7DMU2ATWALZJC/graph.json","fetch_events":"https://pith.science/api/pith-number/RSVXZQNKB454Q7DMU2ATWALZJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC/action/storage_attestation","attest_author":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC/action/author_attestation","sign_citation":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC/action/citation_signature","submit_replication":"https://pith.science/pith/RSVXZQNKB454Q7DMU2ATWALZJC/action/replication_record"}},"created_at":"2026-07-04T15:12:05.643372+00:00","updated_at":"2026-07-04T15:12:05.643372+00:00"}