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On the formal theory of pseudomonads and pseudodistributive laws

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Nicola Gambino and Gabriele Lobbia

We contribute to the formal theory of pseudomonads, i.e. the analogue for pseudomonads of the formal theory of monads. In particular, we solve a problem posed by Lack by proving that, for every Gray-category K, there is a Gray-category Psm(K) of pseudomonads, pseudomonad morphisms, pseudomonad transformations and pseudomonad modifications in K. We then establish a triequivalence between Psm(K) and the Gray-category of pseudomonads introduced by Marmolejo and give a simpler proof of the equivalence between pseudodistributive laws and liftings of pseudomonads to 2-categories of
pseudoalgebras.

Keywords:
pseudomonads, distributive laws, Gray-categories

2020 MSC:
18D05, 18C15, 18C20

*Theory and Applications of Categories,*
Vol. 37, 2021,
No. 2, pp 14-56.

Published 2021-01-20.

http://www.tac.mta.ca/tac/volumes/37/2/37-02.pdf

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