Monoid Homomorphism

DEF-MOH. Monoid Homomorphism.

A monoid homomorphism between two monoids $(M,*,e)$ and $(N,\diamond,i)$ is a function $f:M\to N$ such that:

1. For all $a$, $b\in M$,

   \[f(a*b) = f(a)\diamond f(b).\]
2. \[f(e) = i.\]