A semigroup homomorphism between two semigroups $S$ and $T$ is a function $f : S \to T$ such that for all $a$, $b\in M$,
\[f(ab) = f(a) f(b).\]
A semigroup homomorphism between two semigroups $S$ and $T$ is a function $f : S \to T$ such that for all $a$, $b\in M$,
\[f(ab) = f(a) f(b).\]