{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:36DDMFWJZJFWGZ2NQVC27HIIGQ","short_pith_number":"pith:36DDMFWJ","schema_version":"1.0","canonical_sha256":"df863616c9ca4b63674d8545af9d08342ef49f253567f82075359e3eca2e5600","source":{"kind":"arxiv","id":"1307.0265","version":1},"attestation_state":"computed","paper":{"title":"Skew-monoidal categories and the Catalan simplicial set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mitchell Buckley, Richard Garner, Ross Street, Stephen Lack","submitted_at":"2013-07-01T03:05:29Z","abstract_excerpt":"The basic data for a skew-monoidal category are the same as for a monoidal category, except that the constraint morphisms are no longer required to be invertible. The constraints are given a specific orientation and satisfy Mac Lane's five axioms. Whilst recent applications justify the use of skew-monoidal structure, they do not give an intrinsic justification for the form the structure takes (the orientation of the constraints and the axioms that they satisfy). This paper provides a perspective on skew-monoidal structure which, amongst other things, makes it quite apparent why this particular"},"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":"1307.0265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-01T03:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"c81b6cea2665a2dbc84760630ff5925308bafd65b9fb15a3d72da0dd84c106c1","abstract_canon_sha256":"bebb8e951273adacedbbf84afa133bd40341ad0454af01b9ee002b71a3553186"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:33.826045Z","signature_b64":"FNj/9YOmZTMQ7yZ60RMsfKuY67Tu8NTxmg7ZuN8y3Iwhlb5JGGEOnxplOxXLLl7wAinjj6bNlJ7h8MyPJIIuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df863616c9ca4b63674d8545af9d08342ef49f253567f82075359e3eca2e5600","last_reissued_at":"2026-05-18T03:19:33.825254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:33.825254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew-monoidal categories and the Catalan simplicial set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mitchell Buckley, Richard Garner, Ross Street, Stephen Lack","submitted_at":"2013-07-01T03:05:29Z","abstract_excerpt":"The basic data for a skew-monoidal category are the same as for a monoidal category, except that the constraint morphisms are no longer required to be invertible. The constraints are given a specific orientation and satisfy Mac Lane's five axioms. Whilst recent applications justify the use of skew-monoidal structure, they do not give an intrinsic justification for the form the structure takes (the orientation of the constraints and the axioms that they satisfy). This paper provides a perspective on skew-monoidal structure which, amongst other things, makes it quite apparent why this particular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0265","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":"1307.0265","created_at":"2026-05-18T03:19:33.825384+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0265v1","created_at":"2026-05-18T03:19:33.825384+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0265","created_at":"2026-05-18T03:19:33.825384+00:00"},{"alias_kind":"pith_short_12","alias_value":"36DDMFWJZJFW","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"36DDMFWJZJFWGZ2N","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"36DDMFWJ","created_at":"2026-05-18T12:27:32.513160+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/36DDMFWJZJFWGZ2NQVC27HIIGQ","json":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ.json","graph_json":"https://pith.science/api/pith-number/36DDMFWJZJFWGZ2NQVC27HIIGQ/graph.json","events_json":"https://pith.science/api/pith-number/36DDMFWJZJFWGZ2NQVC27HIIGQ/events.json","paper":"https://pith.science/paper/36DDMFWJ"},"agent_actions":{"view_html":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ","download_json":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ.json","view_paper":"https://pith.science/paper/36DDMFWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0265&json=true","fetch_graph":"https://pith.science/api/pith-number/36DDMFWJZJFWGZ2NQVC27HIIGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/36DDMFWJZJFWGZ2NQVC27HIIGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ/action/storage_attestation","attest_author":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ/action/author_attestation","sign_citation":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ/action/citation_signature","submit_replication":"https://pith.science/pith/36DDMFWJZJFWGZ2NQVC27HIIGQ/action/replication_record"}},"created_at":"2026-05-18T03:19:33.825384+00:00","updated_at":"2026-05-18T03:19:33.825384+00:00"}