Order-adjoint monads and injective objects
Order-adjoint monads and injective objects
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DOI：
10.1016/j.jpaa.2009.08.005
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发表时间：
2010-06
影响因子：
0.8
通讯作者：
G. J. Seal
中科院分区：
文献类型：
--
作者：
G. J. Seal
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.
