{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:BFWII4QTCRJRAKBPKZS5SNKY6V","short_pith_number":"pith:BFWII4QT","schema_version":"1.0","canonical_sha256":"096c847213145310282f5665d93558f552a17722f3f2de84ae245fc18be33307","source":{"kind":"arxiv","id":"2410.05064","version":1},"attestation_state":"computed","paper":{"title":"Operadic Fibrations and Unary Operadic 2-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Dominik Trnka","submitted_at":"2024-10-07T14:21:57Z","abstract_excerpt":"We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction for categorical $\\mathbb{O}$-operads, $\\mathbb{O}$ being a unary operadic category. The construction is a fully faithful functor $\\int_\\mathbb{O}$ which takes categorical $\\mathbb{O}$-operads to operadic functors over $\\mathbb{O}$, and we characterise its essential image by certain lifting properties. Such operadic functors are called operadic fibration. Our theory is an extension of the discrete (unary) operadic case and, in some sense, of the classical Grothendieck construction of a categorical pre"},"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":"2410.05064","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-10-07T14:21:57Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7a057cf5217ab2f0c71ad83e8aeec1afc523f42867aadf553f1a355a87ccb5e4","abstract_canon_sha256":"f95c33bb3aa165baa8ba84028e9326a60e8f8ec6a220786e540ad89bbeb55345"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:17:00.817644Z","signature_b64":"D4wKRjB+R/J1VQRBrkbup4EyUeR6AUWVzFgP+gRO08YH/4LAyZi6jos755HtptP60jjRLoFPMcY75GTspYY0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"096c847213145310282f5665d93558f552a17722f3f2de84ae245fc18be33307","last_reissued_at":"2026-07-05T09:17:00.817158Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:17:00.817158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operadic Fibrations and Unary Operadic 2-categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Dominik Trnka","submitted_at":"2024-10-07T14:21:57Z","abstract_excerpt":"We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction for categorical $\\mathbb{O}$-operads, $\\mathbb{O}$ being a unary operadic category. The construction is a fully faithful functor $\\int_\\mathbb{O}$ which takes categorical $\\mathbb{O}$-operads to operadic functors over $\\mathbb{O}$, and we characterise its essential image by certain lifting properties. Such operadic functors are called operadic fibration. Our theory is an extension of the discrete (unary) operadic case and, in some sense, of the classical Grothendieck construction of a categorical pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.05064","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.05064/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":"2410.05064","created_at":"2026-07-05T09:17:00.817214+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.05064v1","created_at":"2026-07-05T09:17:00.817214+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.05064","created_at":"2026-07-05T09:17:00.817214+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFWII4QTCRJR","created_at":"2026-07-05T09:17:00.817214+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFWII4QTCRJRAKBP","created_at":"2026-07-05T09:17:00.817214+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFWII4QT","created_at":"2026-07-05T09:17:00.817214+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.07083","citing_title":"Predictive Style Matching: Natural and Robust Humanoid Locomotion","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V","json":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V.json","graph_json":"https://pith.science/api/pith-number/BFWII4QTCRJRAKBPKZS5SNKY6V/graph.json","events_json":"https://pith.science/api/pith-number/BFWII4QTCRJRAKBPKZS5SNKY6V/events.json","paper":"https://pith.science/paper/BFWII4QT"},"agent_actions":{"view_html":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V","download_json":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V.json","view_paper":"https://pith.science/paper/BFWII4QT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.05064&json=true","fetch_graph":"https://pith.science/api/pith-number/BFWII4QTCRJRAKBPKZS5SNKY6V/graph.json","fetch_events":"https://pith.science/api/pith-number/BFWII4QTCRJRAKBPKZS5SNKY6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V/action/storage_attestation","attest_author":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V/action/author_attestation","sign_citation":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V/action/citation_signature","submit_replication":"https://pith.science/pith/BFWII4QTCRJRAKBPKZS5SNKY6V/action/replication_record"}},"created_at":"2026-07-05T09:17:00.817214+00:00","updated_at":"2026-07-05T09:17:00.817214+00:00"}