Distributive laws, pseudodistributive laws and decagons.
Charles Walker · arXiv (Cornell University) · 2021
We give alternative definitions of distributive laws and pseudodistributive laws involving the decagonal coherence conditions which naturally arise when the involved monads and pseudomonads are presented in extensive form. We then use these results to give a number of simplifications in the coherence conditions for distributive laws and pseudodistributive laws. In particular, we show that five coherence axioms suffice in the usual definition of pseudodistributive laws, we give simple descriptions of distributive laws and pseudodistributive laws in terms of (pseudo)algebra structure maps, and we give concise definitions of distributive laws and pseudodistributive laws in no-iteration form.