\begin{definition}[Definition:Property of Morphisms Stable Under Composition]
Let $\mathbf C$ be a category.
Let $P$ be a property of morphisms of $\mathbf C$.
Then $P$ is '''stable under composition''' {{iff}}:
:for any three objects $X$, $Y$ and $Z$
:any two morphisms $f, g \in P$ such that $f: X \to Y$ and $g: Y \to Z$
we have:
:$g \circ f \mathop \in P$
Category:Definitions/Category Theory
\end{definition}