For questions related to epimorphisms, which are categorical generalizations of surjective functions.
Definition
A morphism $\varphi\colon X \to Y$ is an epimorphism (epic morphism) if for any object $Z$ and morphisms $f,g \colon Y \to Z$, if $f\varphi=g\varphi$ then $f=g$. This is a categorical generalization of the idea of a surjective function of sets.
