{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CMVAPQIQJLLSPAUG3GWO4QEWZU","short_pith_number":"pith:CMVAPQIQ","schema_version":"1.0","canonical_sha256":"132a07c1104ad7278286d9acee4096cd3e518c79ee6e07383dc123d76a0fea53","source":{"kind":"arxiv","id":"1602.00823","version":2},"attestation_state":"computed","paper":{"title":"Decorated Feynman Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Jason Lucas, Ralph M. Kaufmann","submitted_at":"2016-02-02T08:09:38Z","abstract_excerpt":"In [KW14], the new concept of Feynman categories was introduced to simplify the discussion of operad--like objects. In this present paper, we demonstrate the usefulness of this approach, by introducing the concept of decorated Feynman categories. The procedure takes a Feynman category $\\mathfrak F$ and a functor $\\mathcal O$ to a monoidal category to produce a new Feynman category ${\\mathfrak F}_{dec {\\mathcal O}}$. This in one swat explains the existence of non--sigma operads, non--sigma cyclic operads, and the non--sigma--modular operads of Markl as well as all the usual candidates simply fr"},"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":"1602.00823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-02-02T08:09:38Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"bfee531f7cafcfbc47462191e3a10d828f656b00dafc9bdfcdaca059748b4180","abstract_canon_sha256":"062b236dd77ac00517f2eb8467e89eb2401b2ac448ef83015d143266109a7d64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:49.187606Z","signature_b64":"BtbctfAV2oJGVrQngoNPD9r0oBs1cGPqcltdX1oJEkpKw0SD+Ko3nn7aKlzX1W0peApxRC3oYEUJBDV88EltCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"132a07c1104ad7278286d9acee4096cd3e518c79ee6e07383dc123d76a0fea53","last_reissued_at":"2026-05-18T00:30:49.186786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:49.186786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decorated Feynman Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Jason Lucas, Ralph M. Kaufmann","submitted_at":"2016-02-02T08:09:38Z","abstract_excerpt":"In [KW14], the new concept of Feynman categories was introduced to simplify the discussion of operad--like objects. In this present paper, we demonstrate the usefulness of this approach, by introducing the concept of decorated Feynman categories. The procedure takes a Feynman category $\\mathfrak F$ and a functor $\\mathcal O$ to a monoidal category to produce a new Feynman category ${\\mathfrak F}_{dec {\\mathcal O}}$. This in one swat explains the existence of non--sigma operads, non--sigma cyclic operads, and the non--sigma--modular operads of Markl as well as all the usual candidates simply fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00823","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":""},"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":"1602.00823","created_at":"2026-05-18T00:30:49.186912+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.00823v2","created_at":"2026-05-18T00:30:49.186912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00823","created_at":"2026-05-18T00:30:49.186912+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMVAPQIQJLLS","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMVAPQIQJLLSPAUG","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMVAPQIQ","created_at":"2026-05-18T12:30:09.641336+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/CMVAPQIQJLLSPAUG3GWO4QEWZU","json":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU.json","graph_json":"https://pith.science/api/pith-number/CMVAPQIQJLLSPAUG3GWO4QEWZU/graph.json","events_json":"https://pith.science/api/pith-number/CMVAPQIQJLLSPAUG3GWO4QEWZU/events.json","paper":"https://pith.science/paper/CMVAPQIQ"},"agent_actions":{"view_html":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU","download_json":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU.json","view_paper":"https://pith.science/paper/CMVAPQIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.00823&json=true","fetch_graph":"https://pith.science/api/pith-number/CMVAPQIQJLLSPAUG3GWO4QEWZU/graph.json","fetch_events":"https://pith.science/api/pith-number/CMVAPQIQJLLSPAUG3GWO4QEWZU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU/action/storage_attestation","attest_author":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU/action/author_attestation","sign_citation":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU/action/citation_signature","submit_replication":"https://pith.science/pith/CMVAPQIQJLLSPAUG3GWO4QEWZU/action/replication_record"}},"created_at":"2026-05-18T00:30:49.186912+00:00","updated_at":"2026-05-18T00:30:49.186912+00:00"}