Definition:Property of Morphisms Stable Under Composition

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Definition

Let $\mathbf C$ be a category.

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

Then $P$ is stable under composition if and only if:

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:

$g \circ f \mathop \in P$

Sources

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