[[Monoid object]]
# Homomorphism of monoid objects

Let $M,M'$ be [[Monoid object|monoids]] in $\cat C$.
A **monoid homomorphism** $f : M \to M'$ is a [[homomorphism of semigroup objects]] which additionally satisfies the unitality condition #m/def/cat

![[unital-morphism-string.svg#invert|c]]

These form the morphisms in [[Category of monoid objects]].

#
---
#state/tidy | #lang/en | #SemBr