Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
| Autor: | Juan L. López Hernández, Luis Jesuacuteis Turcio, Adrian Vazquez-Marquez |
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| Rok vydání: | 2018 |
| Předmět: |
2-adjunctions
Pure mathematics Property (philosophy) lcsh:Mathematics Applied Mathematics Structure (category theory) monad theory liftings for algebras Type (model theory) lcsh:QA1-939 Adjunction Monad (functional programming) Mathematics::Algebraic Topology monoidal monads Computational Mathematics Computer Science::Logic in Computer Science Mathematics::Category Theory Discrete Mathematics and Combinatorics Bijection injection and surjection Computer Science::Databases Analysis 2-categories Mathematics |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 10, Iss 1, Pp 117-156 (2019) |
| ISSN: | 2345-5861 2345-5853 |
| DOI: | 10.29252/cgasa.10.1.117 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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