TITLE: The inclusion $\mathbb Z \to \mathbb Q$ is an epimorphism
QUESTION [6 upvotes]: I am supposed to show that the inclusion of the integers in the rationals is an epimorphism in the category of abelian groups. Not only am I unable to find the right argument, I am starting to wonder if it is true at all.
Any thoughts or counter-examples?
Thank you.

REPLY [8 votes]: This is false in the category of abelian groups. Consider the composition $\mathbb Z \hookrightarrow \mathbb Q \to \mathbb Q / \mathbb Z$.