000172838 001__ 172838
000172838 005__ 20181203022605.0
000172838 022__ $$a0022-4049
000172838 02470 $$2ISI$$a000274928100006
000172838 0247_ $$2doi$$a10.1016/j.jpaa.2009.08.005
000172838 037__ $$aARTICLE
000172838 245__ $$aOrder-adjoint monads and injective objects
000172838 269__ $$a2010
000172838 260__ $$bElsevier$$c2010
000172838 336__ $$aJournal Articles
000172838 520__ $$aGiven a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T is shown to be strictly monadic over the category of Kleisli monoids. If the Kleisli category of T moreover forms an order-enriched category. then the monad induced by the new situation is Kock-Zoberlein. Injective objects in the category of Kleisli monoids with respect to the class of initial morphisms then characterize the objects of the Eilenberg-Moore category of T, a fact that allows us to recuperate a number of known results, and present some new ones. (C) 2009 Elsevier B.V. All rights reserved.
000172838 6531_ $$aAlgebras
000172838 6531_ $$aLattices
000172838 700__ $$aSeal, Gavin J.
000172838 773__ $$j214$$tJournal Of Pure And Applied Algebra$$q778-796
000172838 909C0 $$xU10968$$0252139$$pUPHESS
000172838 909CO $$pSV$$particle$$ooai:infoscience.tind.io:172838
000172838 917Z8 $$x105396
000172838 937__ $$aEPFL-ARTICLE-172838
000172838 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000172838 980__ $$aARTICLE