{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T23:55:39Z","timestamp":1771458939945,"version":"3.50.1"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"7","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"unspecified","delay-in-days":117,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Finitary monads on <jats:monospace>Pos<\/jats:monospace> are characterized as precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequations in context. Analogously, finitary enriched monads on <jats:monospace>Pos<\/jats:monospace> are characterized: here we work with varieties of coherent algebras which means that their operations are monotone.<\/jats:p>","DOI":"10.1017\/s0960129521000360","type":"journal-article","created":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T03:58:33Z","timestamp":1637899113000},"page":"799-821","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["Finitary monads on the category of posets"],"prefix":"10.1017","volume":"31","author":[{"given":"Ji\u0159\u00ed","family":"Ad\u00e1mek","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3892-5917","authenticated-orcid":false,"given":"Chase","family":"Ford","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2021-1644","authenticated-orcid":false,"given":"Stefan","family":"Milius","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3146-5906","authenticated-orcid":false,"given":"Lutz","family":"Schr\u00f6der","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,11,26]]},"reference":[{"key":"S0960129521000360_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(76)80030-X"},{"key":"S0960129521000360_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600579"},{"key":"S0960129521000360_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S096012951500050X"},{"key":"S0960129521000360_ref25","first-page":"332","volume-title":"Mathematical Foundations of Programming Semantics, MFPS 2001","volume":"45","author":"Plotkin","year":"2001"},{"key":"S0960129521000360_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00019-5"},{"key":"S0960129521000360_ref27","first-page":"83","article-title":"Enriched Lawvere theories","volume":"6","author":"Power","year":"1999","journal-title":"Theory and Applications of Categories"},{"key":"S0960129521000360_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01111838"},{"key":"S0960129521000360_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0083080"},{"key":"S0960129521000360_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/LICS52264.2021.9470517"},{"key":"S0960129521000360_ref2","doi-asserted-by":"crossref","unstructured":"Ad\u00e1mek, J. , Dost\u00e1l, M. and Velebil, J. (2021). A categorical view of varieties of ordered algebras. Mathematical Structures in Computer Science, special issue in honor of John Power, to appear, available at https:\/\/arxiv.org\/abs\/2011.13839.","DOI":"10.1017\/S0960129521000463"},{"key":"S0960129521000360_ref31","unstructured":"Rosick\u00fd, J. (2021). Metric monads. Submitted, available at https:\/\/arxiv.org\/abs\/2012.14641."},{"key":"S0960129521000360_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00872987"},{"key":"S0960129521000360_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(91)90052-4"},{"key":"S0960129521000360_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9860-1"},{"key":"S0960129521000360_ref1","first-page":"589","article-title":"Free algebras and automata realizations in the language of categories","volume":"15","author":"Ad\u00e1mek","year":"1974","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0960129521000360_ref8","volume-title":"Encyclopedia of Mathematics and its Applications","author":"Borceux","year":"1994"},{"key":"S0960129521000360_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(83)90080-4"},{"key":"S0960129521000360_ref29","first-page":"109","article-title":"Positively convex modules and ordered normed linear spaces","volume":"10","author":"Pumpl\u00fcn","year":"2003","journal-title":"Journal of Convex Analysis"},{"key":"S0960129521000360_ref11","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.1989.39173"},{"key":"S0960129521000360_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2008.07.009"},{"key":"S0960129521000360_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700006353"},{"key":"S0960129521000360_ref10","unstructured":"Ford, C. , Milius, S. and Schr\u00f6der, L. (2021b). Monads on categories of relational structures. In: Gadducci, F. and Silva, A. (eds.) Algebra and Coalgebra in Computer Science, CALCO 2021, LIPIcs, Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik. To appear. Full version available as arXiv e-print 2107.03880."},{"key":"S0960129521000360_ref21","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2017.8005102"},{"key":"S0960129521000360_ref30","doi-asserted-by":"publisher","DOI":"10.1080\/00927878408823035"},{"key":"S0960129521000360_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45931-6_24"},{"key":"S0960129521000360_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-17127-8_23"},{"key":"S0960129521000360_ref32","first-page":"339","article-title":"Free algebras, input processes and free monads","volume":"16","author":"Trnkov\u00e1","year":"1975","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0960129521000360_ref28","volume-title":"LNCS","volume":"3629","author":"Power","year":"2005"},{"key":"S0960129521000360_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(93)90092-8"},{"key":"S0960129521000360_ref18","volume-title":"Categories for the Working Mathematician","author":"MacLane","year":"1998"},{"key":"S0960129521000360_ref5","unstructured":"Bird, R. (1984). Limits in 2-Categories of Locally Presentened Categories. Phd thesis, University of Sydney."},{"key":"S0960129521000360_ref20","first-page":"700","volume-title":"Logic in Computer Science, LICS 2016","author":"Mardare","year":"2016"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129521000360","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T12:56:47Z","timestamp":1646053007000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129521000360\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8]]},"references-count":32,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["S0960129521000360"],"URL":"https:\/\/doi.org\/10.1017\/s0960129521000360","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}