Geodesic
Classifiers for monad morphisms and adjunction morphisms
Theory and applications of categories, Tome 32 (2017), pp. 1050-1097.

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We provide an explicit model for the free 2-category containing n composable adjunction morphisms, comparable to the Schanuel and Street model for the free adjunction. We can extract from it an explicit model for the free 2-category containing n composable lax monad morphisms. A careful proof is given, which goes through presentations of the hom-categories of our model. We use one of these hom-categories as an indexing category to construct an extended Artin-Mazur codiagonal, whose underlying bisimplicial set has the classical Artin-Mazur codiagonal as its first column.
Publié le :
Classification : 18C15, 18D05, 18G30, 55U10, 55U35
Keywords: monad, adjunction, 2-category, Artin-Mazur codiagonal 
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     author = {Dimitri Zaganidis},
     title = {Classifiers for monad morphisms and adjunction morphisms},
     journal = {Theory and applications of categories},
     pages = {1050--1097},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a30/}
}
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Dimitri Zaganidis. Classifiers for monad morphisms and adjunction morphisms. Theory and applications of categories, Tome 32 (2017), pp. 1050-1097. http://geodesic.mathdoc.fr/item/TAC_2017_32_a30/