On the formal theory of pseudomonads and pseudodistributive laws
Nicola Gambino, Gabriele Lobbia · Theory and applications of categories · 2021
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 2categories of pseudoalgebras.