Let $\matrix{ A& \mathop{\longrightarrow}\limits^f &B\\\\
 \Big\downarrow & & \Big\downarrow\\\\ 
 C& \mathop{\longrightarrow}\limits\_g &D}$ 
be a pushout diagram in a category $\mathcal C$.


If $f$ is monic, is $g$ also monic? How to prove this easily? Thanks.



Do pushouts preserve monic?
This is true, for example, in topoi and in abelian categories, but it fails in general: In $C=\mathsf{CRing}$ we have a pushout


$\matrix{ \mathbb{Z} & \longrightarrow & \mathbb{Q}\\\\
 \downarrow & & \downarrow\\\\ 
 \mathbb{Z}/2 & \longrightarrow & 0.}$ 


