Example 9.1.2.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$ which contains a pair of composable morphisms $f: X \rightarrow Y$ and $g: Y \rightarrow Z$. Then any composition of $f$ with $g$ is a transfinite composition of morphisms of $W$ (take $\alpha = 2$ in Definition 1.5.4.10). In particular, if $W$ is closed under transfinite composition, then it is closed under composition.
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