Another characterization of no-iteration distributive laws

TL;DR

This paper characterizes no-iteration distributive laws using monads in extensive form, incorporating both right and left extension systems, and describes related 1-cell and 2-cell structures.

Contribution

It introduces a new characterization of no-iteration distributive laws through monads in extensive form, considering both extension systems and their categorical morphisms.

Findings

Provides a new perspective on no-iteration distributive laws

Characterizes 1-cells and 2-cells in EM and Kl categories

Integrates right and left extension systems in the characterization

Abstract

We provide a characterization of no-iteration distributive laws in terms of its monads in extensive form only. To do that, it is necessary to take account of both right and left extension systems. We also give, in this right-left perspective, characterizations of the 1-cells and 2-cells in $\mathbf{EM}(K)$ and $\mathbf{Kl}(K)$.