Definition:Property of Morphisms Stable Under Composition

Definition
Let $\mathbf C$ be a category.

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

Then $P$ is stable under composition :
 * 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:
 * $g \circ f \mathop \in P$