Presentations of pseudodistributive laws

Abstract

By considering the situation in which the involved pseudomonads are presented in no-iteration form, we deduce a number of alternative presentations of pseudodistributive laws including a 'decagon' form, a pseudoalgebra form, a no-iteration form, and a warping form. As an application, we show that five coherence axioms suffice in the usual monoidal definition of a pseudodistributive law.