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We show that monad-comonad interaction laws are an instance of measuring maps from Sweedler theory for duoidal categories whereby the final interacting comonad for a monad and a residual monad arises as the Sweedler hom and the initial residual monad for a monad and an interacting comonad as the Sweedler copower. We then combine this with a (co)algebraic characterization of monad-comonad interaction laws to derive descriptions of the Sweedler hom and the Sweedler copower in terms of their coalgebras resp. algebras.<\/jats:p>","DOI":"10.1007\/978-3-030-99253-8_22","type":"book-chapter","created":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T20:02:48Z","timestamp":1648497768000},"page":"428-448","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sweedler Theory of Monads"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6705-1449","authenticated-orcid":false,"given":"Dylan","family":"McDermott","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2114-624X","authenticated-orcid":false,"given":"Exequiel","family":"Rivas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1297-0579","authenticated-orcid":false,"given":"Tarmo","family":"Uustalu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,29]]},"reference":[{"key":"22_CR1","unstructured":"Ad\u00e1mek, J., Rosick\u00fd, J.: Locally Presentable and Accessible Categories, London Math. 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