Applications of the Kleisli and Eilenberg-Moore 2-adjunctions

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Lopez Hernandez J.L.; Turcio Cuevas L.J.; Vazquez Marquez a.

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Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2019 | Volume:10 | Issue:1 Page(s): 117-156

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Information Journal Paper

Title

Applications of the Kleisli and Eilenberg-Moore 2-adjunctions

Author(s)

Lopez Hernandez J.L. | Turcio Cuevas L.J. | Vazquez Marquez a. | Issue Writer Certificate

Keywords

2-categoriesQ4

2-adjunctionsQ4

monad theoryQ4

liftings for algebrasQ4

monoidal monadsQ4

Abstract

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.

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APA: Copy

Lopez Hernandez, J.L., Turcio Cuevas, L.J., & Vazquez Marquez, a.. (2019). Applications of the Kleisli and Eilenberg-Moore 2-adjunctions. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 10(1 ), 117-156. SID. https://sid.ir/paper/255417/en

Vancouver: Copy

Lopez Hernandez J.L., Turcio Cuevas L.J., Vazquez Marquez a.. Applications of the Kleisli and Eilenberg-Moore 2-adjunctions. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2019;10(1 ):117-156. Available from: https://sid.ir/paper/255417/en

IEEE: Copy

J.L. Lopez Hernandez, L.J. Turcio Cuevas, and a. Vazquez Marquez, “Applications of the Kleisli and Eilenberg-Moore 2-adjunctions,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 10, no. 1 , pp. 117–156, 2019, [Online]. Available: https://sid.ir/paper/255417/en

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