TY - EJOUR
DO - 10.1016/j.jpaa.2009.08.005
AB - 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.
T1 - Order-adjoint monads and injective objects
DA - 2010
AU - Seal, Gavin J.
JF - Journal Of Pure And Applied Algebra
SP - 778-796
VL - 214
EP - 778-796
PB - Elsevier
ID - 172838
KW - Algebras
KW - Lattices
SN - 0022-4049
ER -