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

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 18D05, 18C15, 18C20
Keywords: pseudomonads, distributive laws, Gray-categories 
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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/