Geodesic
Dense morphisms of monads
Theory and applications of categories, Tome 18 (2007), pp. 372-399.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Given an arbitrary locally finitely presentable category $K$ and finitary monads $T$ and $S$ on $K$, we characterize monad morphisms $\alpha: S\to T$ with the property that the induced functor $\alpha_*: K^T \to K^ S$ between the categories of Eilenberg-Moore algebras is fully faithful. We call such monad morphisms dense and give a characterization of them in the spirit of Beth's definability theorem: $\alpha$ is a dense monad morphism if and only if every $T$-operation is explicitly defined using $S$-operations. We also give a characterization in terms of epimorphic property of $\alpha$ and clarify the connection between various notions of epimorphisms between monads.
Classification : 18C20, 18C35
Keywords: Definable operation, monad morphism, locally finitely presentable category 
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     author = {Panagis Karazeris and Jiri Velebil},
     title = {Dense morphisms of monads},
     journal = {Theory and applications of categories},
     pages = {372--399},
     publisher = {mathdoc},
     volume = {18},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a13/}
}
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Panagis Karazeris; Jiri Velebil. Dense morphisms of monads. Theory and applications of categories, Tome 18 (2007), pp. 372-399. http://geodesic.mathdoc.fr/item/TAC_2007_18_a13/