In category theory, a monomorphism is a situation where
$g: A \rightarrow B \;\;$ , $\;\;h: A \rightarrow B\;\;$ and $\;\;f:B \rightarrow C$
$f \circ g = f \circ h \;\text{ imples in } \; g = h$
I heard recently something about monomorphism to be an injective homomorphism , but it didn't make sense to me and I still couldn't prove it.
How can I prove that monomorphism is an injective homomorphism (at least for monoids)?