A monoid homomorphism between two monoids $M$ and $N$ is a function $f : M \to N$ such that:
For all $a$, $b \in M$,
\[f(ab) = f(a) f(b).\]If $e$ and $i$ are respectively the neutral elements of $M$ and $N$,
\[f(e) = i.\]
A monoid homomorphism between two monoids $M$ and $N$ is a function $f : M \to N$ such that:
For all $a$, $b \in M$,
\[f(ab) = f(a) f(b).\]If $e$ and $i$ are respectively the neutral elements of $M$ and $N$,
\[f(e) = i.\]