Monic

In Category Theory, a monic or monomorphisms is any morphism $f$ such that the following is a pullback:

\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
A \arrow[d, "1_A"] \arrow[r, "1_A"] & A \arrow[d, "f"] \\
A \arrow[r, "f"] & B
\end{tikzcd}
\end{document}

Remarks

In Set, monomorphisms are simply just the injective functions.