Definition:Property of Morphisms Stable Under Pullback

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Let $\mathbf C$ be a category.

Let $P$ be a property of morphisms of $\mathbf C$.

Then $P$ is stable under pullback if and only if:

for all morphisms $f : X \to Y$ with $f \mathop \in P$
for all morphisms $g : Z \to Y$ for which the pullback of $f$ and $g$
$\begin{xy}\[email protected]+2mu@+1em{ X \times_Y Z \ar[r] \ar[d]^{f'} & X \ar[d]^f \\ Z \ar[r]^g & Y }\end{xy}$

we have that $f' \in P$.