Warning 9.2.5.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a pair of morphisms $f: A \rightarrow B$ and $g: X \rightarrow Y$. If $f$ is weakly left orthogonal to $g$ in the $\infty $-category $\operatorname{\mathcal{C}}$, then the homotopy class $[f]$ is weakly left orthogonal to $[g]$ in the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ (see Exercise 1.5.2.10). Beware that the converse is false in general (see Warning 9.2.5.5 and Exercise 9.2.5.6).
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