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A biwreath is then a system containing a wreath, a cowreath and their mixed versions, but also a 2-cell $\\lambda$ in $\\bEM(\\K)$ governing the compatibility of the monad and the comonad structure of the biwreath. We deduce that the monad laws encode 2-(co)cycles and the comonad laws so called 3-(co)cycles, while the 2-cell conditions of the (co)monad structure 2-cells of the biwreath encode (co)actions twisted by these"},"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":"1707.05447","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-07-18T03:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"92915dc64c988dffe3a8e2c3fd0b0703ab057ec1f27954831df784c7de229bc2","abstract_canon_sha256":"d625fd1bf982f6be4e9700189c4e1bca7849def6a99ed770dad40061b7000459"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:17.730196Z","signature_b64":"kbJYIc8N3ZBVzHJ8wj2bFO6Qp1jGPN3CdPRrHcJQTxVByc2oh8FToIXuZfgQjlsKmtRgB0pc3oGYP2OmFdgdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03efda243fe6e7fa7595e9d7211e7321aadf3c5a7d86687807c9669c6c45e9e6","last_reissued_at":"2026-05-18T00:38:17.729570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:17.729570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biwreaths: a self-contained system in a 2-category that encodes different known algebraic constructions and gives rise to new ones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bojana Femi\\'c","submitted_at":"2017-07-18T03:14:05Z","abstract_excerpt":"We introduce bimonads in a 2-category $\\K$ and define biwreaths as bimonads in the 2-category $\\bEM(\\K)$ of bimonads, in the analogous fashion as Lack and Street defined wreaths. 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