172838
20181203022605.0
0022-4049
ISI
000274928100006
doi
10.1016/j.jpaa.2009.08.005
ARTICLE
Order-adjoint monads and injective objects
2010
Elsevier
2010
Journal Articles
Given 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.
Algebras
Lattices
Seal, Gavin J.
214
778-796
Journal Of Pure And Applied Algebra
252139
UPHESS
U10968
oai:infoscience.tind.io:172838
SV
article
105396
EPFL-ARTICLE-172838
EPFL
REVIEWED
PUBLISHED
ARTICLE