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Classifiers for monad morphisms and adjunction morphisms

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Dimitri Zaganidis

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.

Published 2017-08-23.

http://www.tac.mta.ca/tac/volumes/32/31/32-31.pdf

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