Presentations of pseudodistributive laws

TL;DR

This paper explores various alternative presentations of pseudodistributive laws in category theory, simplifying coherence axioms and providing new perspectives on their structure and applications.

Contribution

It introduces multiple new forms of pseudodistributive laws, including a decagon and warping form, and reduces the coherence axioms needed in their monoidal definition.

Findings

Five coherence axioms suffice in the monoidal definition

Introduces a decagon form of pseudodistributive laws

Provides alternative presentations including pseudoalgebra and warping forms

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.