Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
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.<br />Since any 2...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2019-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | http://www.cgasa.ir/article_76725_4c74fe2ffb149c7099e49e4c27eeb355.pdf |
| Summary: | 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.<br />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.<br />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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| ISSN: | 2345-5853 2345-5861 |