In Category Theory, a epic or epimorphisms is any morphism such that the following is a pushout:
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
A \arrow[d, "f"] \arrow[r, "f"] & B \arrow[d, "1_B"] \\
B \arrow[r, "1_B"] & B
\end{tikzcd}
\end{document}Remarks
In Set, epimorphisms are simply just the surjective functions.