= Pullback stability of epimorphisms in an abelian category
In an <abelian category>, the <pullback in a category> of an <epimorphism> $p:B\to C$ along $k:C'\to C$ is the kernel of the epimorphism $[p,-k]:B\oplus C'\to C$. If $v:C'\to D$ annihilates its projection, $[0,v]$ annihilates that kernel and therefore factors through $[p,-k]$. Restriction to $B$ forces the factor to vanish, giving $v=0$ and proving the projection epic. This uses the definition's normality of epimorphisms.
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