Geodesic
On the formal theory of pseudomonads and pseudodistributive laws
Theory and applications of categories, Tome 37 (2021), pp. 14-56
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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.

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Classification : 18D05, 18C15, 18C20
Keywords: pseudomonads, distributive laws, Gray-categories 
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     author = {Nicola Gambino and Gabriele Lobbia},
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Nicola Gambino; Gabriele Lobbia. On the formal theory of pseudomonads and pseudodistributive laws. Theory and applications of categories, Tome 37 (2021), pp. 14-56. http://geodesic.mathdoc.fr/item/TAC_2021_37_a1/