TY - JOUR
ID - 76725
TI - Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - L\'opez Hernández, Juan Luis
AU - Turcio, Luis Jesús
AU - Vazquez-Marquez, Adrian
AD - Research Coordination, CINVCAT, P.O. Box 36620, Irapuato, Gto. M\'exico.
AD - Instituto de Matemáticas, UNAM
AD - Research Coordination, Universidad Incarnate Word Campus Bajío, P.O. Box 36821, Irapuato, Gto. M\'exico.
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 117
EP - 156
KW - 2-categories
KW - 2-adjunctions
KW - monad theory
KW - liftings for algebras
KW - monoidal monads
DO - 10.29252/cgasa.10.1.117
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_76725.html
L1 - https://cgasa.sbu.ac.ir/article_76725_4c74fe2ffb149c7099e49e4c27eeb355.pdf
ER -