Definition:Property of Morphisms Stable Under Pullback

Definition
Let $\mathbf C$ be a category.

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

Then $P$ is stable under pullback :
 * 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}\xymatrix@L+2mu@+1em{

X \times_Y Z \ar[r] \ar[d]^{f'} & X \ar[d]^f \\ Z \ar[r]^g & Y }\end{xy}$
 * exists

we have that $f' \in P$.