doi:10.1016/j.jpaa.2009.08.005
ISI:000274928100006
Seal, Gavin J.
Order-adjoint monads and injective objects
, Elsevier
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.
2011-12-16T14:00:09Z
http://infoscience.epfl.ch/record/172838
http://infoscience.epfl.ch/record/172838
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