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 $Z$ and any two morphisms $f : X \to Y$ and $g : Y \to Z$ with $f,g \mathop \in P$, we have $g \circ f \mathop \in P$.