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 the neutral elements of $M$ and $N$ respectively,
\[f(e) = i.\]
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 the neutral elements of $M$ and $N$ respectively,
\[f(e) = i.\]