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.
Keywords: monad, adjunction, 2-category, Artin-Mazur codiagonal
2010 MSC: 18C15, 18D05,18G30, 55U10,55U35
Theory and Applications of Categories, Vol. 32, 2017, No. 31, pp 1050-1097.