# Why do we need the condition “cocommutative” in the definition of a coPoisson Hopf algebra?

In this paper, page 5, Section 3.6, in the definition of a coPoisson Hopf algebra $H$, it is said that: a coPoisson Hopf algebra is a cocommutative Hopf algebra $A$ with a map $\delta: A \to A \otimes A$ which satisfies some properties. Why do we need the condition "cocommutative" in the definition of a coPoisson Hopf algebra?