Remark 8.5.1.6 (Transitivity). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing objects $X$, $Y$, and $Z$. If $Y$ is a retract of $X$ and $Z$ is a retract of $Y$, then $Z$ is a retract of $X$. To prove this, it suffices to establish the analogous result for the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ (Remark 8.5.1.2), which follows immediately from Remark 8.5.0.1.
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