[[Comonoid object]]
# Homomorphism of comonoid objects

Given [[Comonoid object|comonoids]] $C,C'$ in $\cat C$, a morphism $f : C \to C'$ is a **comonoid homomorphism** iff $\op f: C' \to C$ is a [[homomorphism of monoid objects]] in $\op{\cat C}$. #m/def/cat 
Thus we have

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

and

![[coünital-morphism-string.svg#invert]]

These are the morphisms in [[Category of comonoid objects]].

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