We extend the classical work of Kock on strong and commutative monads, as well as the work of Hyland and Power for 2-monads, in order to define strong and pseudocommutative relative pseudomonads. To achieve this, we work in the more general setting of 2-multicategories rather than monoidal 2-categories. We prove analogous implications to the classical work: that a strong relative pseudomonad is a pseudo-multifunctor, and that a pseudocommutative relative pseudomonad is a multicategorical pseudomonad. Furthermore, we extend the work of López Franco with a proof that a lax-idempotent strong relative pseudomonad is pseudocommutative.
We apply the results of this paper to the example of the presheaf relative pseudomonad.
Keywords: category theory, monad theory, presheaf
@article{TAC_2023_39_a33,
author = {Andrew Slattery},
title = {Pseudocommutativity and lax idempotency for relative pseudomonads},
journal = {Theory and applications of categories},
pages = {1018--1049},
year = {2023},
volume = {39},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/}
}
Andrew Slattery. Pseudocommutativity and lax idempotency for relative pseudomonads. Theory and applications of categories, Tome 39 (2023), pp. 1018-1049. http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/