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We demonstrate that even when working at this high level of generality, one can obtain useful results. In particular, we give conditions under which one can obtain free monoids and Cayley representations at the level of monoidal categories, and we show that their concretisation results in useful constructions for monads, applicative functors, and arrows. Moreover, by taking advantage of the uniform presentation of the three notions of computation, we introduce a principled approach to the analysis of the relation between them.<\/jats:p>","DOI":"10.1017\/s0956796817000132","type":"journal-article","created":{"date-parts":[[2017,10,5]],"date-time":"2017-10-05T04:34:49Z","timestamp":1507178089000},"source":"Crossref","is-referenced-by-count":17,"title":["Notions of computation as monoids"],"prefix":"10.46298","volume":"27","author":[{"given":"EXEQUIEL","family":"RIVAS","sequence":"first","affiliation":[]},{"given":"MAURO","family":"JASKELIOFF","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,10,5]]},"reference":[{"key":"S0956796817000132_ref20","first-page":"159","volume-title":"Summer School on Advanced Functional Programming 2002, Oxford University","author":"Hudak","year":"2003"},{"key":"S0956796817000132_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2010.01.025"},{"key":"S0956796817000132_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(90)90151-7"},{"key":"S0956796817000132_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0021-0"},{"key":"S0956796817000132_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00590-9_6"},{"key":"S0956796817000132_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2011.02.018"},{"key":"S0956796817000132_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(86)90059-1"},{"key":"S0956796817000132_ref46","doi-asserted-by":"crossref","unstructured":"Voigtl\u00e4nder J. (2008) Asymptotic improvement of computations over free monads. In Proceedings of the 9th International Conference on Mathematics of Program Construction, Audebaud P. & Paulin-Mohring C. (eds), Lecture Notes in Computer Science, vol. 5133. 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