{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T23:05:35Z","timestamp":1779836735480,"version":"3.53.1"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3-4","license":[{"start":{"date-parts":[[2009,7,1]],"date-time":"2009-07-01T00:00:00Z","timestamp":1246406400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Funct. Prog."],"published-print":{"date-parts":[[2009,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Motivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads on\n                    <jats:italic>Set<\/jats:italic>\n                    . We generalise that relationship from\n                    <jats:italic>Set<\/jats:italic>\n                    to an arbitrary locally presentable category such as\n                    <jats:italic>Poset<\/jats:italic>\n                    and \u03c9\n                    <jats:italic>Cpo<\/jats:italic>\n                    or functor categories such as [\n                    <jats:italic>Inj<\/jats:italic>\n                    ,\n                    <jats:italic>Set<\/jats:italic>\n                    ] and [\n                    <jats:italic>Inj<\/jats:italic>\n                    , \u03c9\n                    <jats:italic>Cpo<\/jats:italic>\n                    ]. That involves allowing the arities of Lawvere theories to be extended to being size-restricted objects of the locally presentable category. We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel\u2013Ulmer duality.\n                  <\/jats:p>","DOI":"10.1017\/s0956796809007254","type":"journal-article","created":{"date-parts":[[2009,6,9]],"date-time":"2009-06-09T10:05:04Z","timestamp":1244541904000},"page":"265-286","source":"Crossref","is-referenced-by-count":8,"title":["Gabriel\u2013Ulmer duality and Lawvere theories enriched over a general base"],"prefix":"10.1017","volume":"19","author":[{"given":"STEPHEN","family":"LACK","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JOHN","family":"POWER","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,7,1]]},"reference":[{"key":"S0956796809007254_ref21","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1995.1112"},{"key":"S0956796809007254_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(91)90052-4"},{"key":"S0956796809007254_ref12","first-page":"3","article-title":"Structures defined by finite limits in the enriched context I","volume":"23","author":"Kelly","year":"1982","journal-title":"Cahiers Topol. G\u00e9om. Diff\u00e9r. Cat\u00e9g."},{"key":"S0956796809007254_ref11","volume-title":"Basic Concepts of Enriched Category Theory","author":"Kelly","year":"1982"},{"key":"S0956796809007254_ref14","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/3-540-45988-X_3","volume-title":"Proceedings of the 4th International Workshop on Frontiers of Combining Systems, FroCoS 2002 (Santa Margherita Ligure, April 2002)","author":"L\u00fcth","year":"2002"},{"key":"S0956796809007254_ref10","first-page":"153","article-title":"Pullbacks equivalent to pseudo-pullbacks","volume":"34","author":"Joyal","year":"1993","journal-title":"Cahiers Topol. G\u00e9om. Diff\u00e9r. Cat\u00e9g."},{"key":"S0956796809007254_ref4","first-page":"42","volume-title":"Advanced Lectures from International Summer School on Applied Semantics, APPSEM 2000 (Caminha, September 2000)","author":"Benton","year":"2002"},{"key":"S0956796809007254_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.07.007"},{"key":"S0956796809007254_ref15","first-page":"14","volume-title":"Proceedings of the 4th Annual IEEE Symposium on Logic in Computer Science, LICS '89 (Pacific Grove, CA, June 1989)","author":"Moggi","year":"1989"},{"key":"S0956796809007254_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600579"},{"key":"S0956796809007254_ref3","volume-title":"Category Theory for Computing Science","author":"Barr","year":"1990"},{"key":"S0956796809007254_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2008.07.009"},{"key":"S0956796809007254_ref19","first-page":"342","volume-title":"Proceedings of the 5th International Confernce on Foundations of Software Science and Computation Structures, FOSSACS 2002 (Grenoble, April 2002)","author":"Plotkin","year":"2002"},{"key":"S0956796809007254_ref20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023064908962"},{"key":"S0956796809007254_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.03.013"},{"key":"S0956796809007254_ref9","first-page":"437","volume-title":"Computation, Meaning, and Logic: Articles Dedicated to Gordon Plotkin","author":"Hyland","year":"2007"},{"key":"S0956796809007254_ref18","volume-title":"Algol-Like Languages","author":"O'Hearn","year":"1997"},{"key":"S0956796809007254_ref13","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.50.5.869"},{"key":"S0956796809007254_ref22","first-page":"83","article-title":"Enriched Lawvere theories","volume":"6","author":"Power","year":"2000","journal-title":"Theory Appl. Categ."},{"key":"S0956796809007254_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s001650200014"},{"key":"S0956796809007254_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0021-0"},{"key":"S0956796809007254_ref5","first-page":"21","volume-title":"Proceedings of the 19th Internatinal Colloquium in Trees in Algebra and Programming, CAAP '94 (Edinburgh, April 1994)","author":"Heckmann","year":"1994"},{"key":"S0956796809007254_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.12.026"},{"key":"S0956796809007254_ref23","first-page":"355","volume-title":"Proceedings of the 22nd Annual Conference on Mathematical Foundations of Programming Semantics, MFPS-XXII (Genova, May 2006)","author":"Power","year":"2006"}],"container-title":["Journal of Functional Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0956796809007254","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T22:35:57Z","timestamp":1779834957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0956796809007254\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":24,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0956796809007254"],"URL":"https:\/\/doi.org\/10.1017\/s0956796809007254","relation":{},"ISSN":["0956-7968","1469-7653"],"issn-type":[{"value":"0956-7968","type":"print"},{"value":"1469-7653","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}