Let $G$ and $H$ each be a D265: Monoid such that

(i)	$1_G$ and $1_H$ are each an D39: Identity element in $G$ and $H$, respectively

A D18: Map $f : G \to H$ is a monoid homomorphism from $G$ to $H$ if and only if

(1)	\begin{equation} \forall \, x, y \in G : f(x y) = f(x) f(y) \end{equation}
(2)	\begin{equation} f(1_G) = 1_H \end{equation}