%0 Journal Article
%T Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A L\'opez Hernández, Juan Luis
%A Turcio, Luis Jesús
%A Vazquez-Marquez, Adrian
%D 2019
%\ 01/01/2019
%V 10
%N 1
%P 117-156
%! Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
%K 2-categories
%K 2-adjunctions
%K monad theory
%K liftings for algebras
%K monoidal monads
%R 10.29252/cgasa.10.1.117
%X In 2010, J. Climent Vidal and J. Soliveres Tur developed, among other things, a pair of 2-adjunctions between the 2-category of adjunctions and the 2-category of monads. One is related to the Kleisli adjunction and the other to the Eilenberg-Moore adjunction for a given monad.Since any 2-adjunction induces certain natural isomorphisms of categories, these can be used to classify bijections and isomorphisms for certain structures in monad theory. In particular, one important example of a structure, lying in the 2-category of adjunctions, where this procedure can be applied to is that of a lifting. Therefore, a lifting can be characterized by the associated monad structure,lying in the 2-category of monads, through the respective 2-adjunction. The same can be said for Kleisli extensions.Several authors have been discovered this type of bijections and isomorphisms but these pair of 2-adjunctions can collect them all at once with an extra property, that of naturality.
%U https://cgasa.sbu.ac.ir/article_76725_4c74fe2ffb149c7099e49e4c27eeb355.pdf