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- W2055871932 abstract "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–Zöberlein. 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." @default.
- W2055871932 created "2016-06-24" @default.
- W2055871932 creator A5068361496 @default.
- W2055871932 date "2010-06-01" @default.
- W2055871932 modified "2023-10-02" @default.
- W2055871932 title "Order-adjoint monads and injective objects" @default.
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- W2055871932 doi "https://doi.org/10.1016/j.jpaa.2009.08.005" @default.
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