\begin{definition}[Definition:Property of Morphisms Stable Under Pullback]
Let $\mathbf C$ be a category.
Let $P$ be a property of morphisms of $\mathbf C$.
Then $P$ is '''stable under pullback''' {{iff}}:
: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 $f' \in P$.
Category:Definitions/Category Theory
\end{definition}