Corollary 9.2.7.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing morphisms $f: A \rightarrow B$ and $g: X \rightarrow Y$. If either $f$ or $g$ is an isomorphism, then $f$ is left orthogonal to $g$.
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Proof. Without loss of generality, we may assume that $f$ is an isomorphism. Let $\pi : \operatorname{\mathcal{C}}_{/Y} \rightarrow \operatorname{\mathcal{C}}$ be the projection map, so that we can identify $g$ with an object $\widetilde{X} \in \operatorname{\mathcal{C}}_{/Y}$ satisfying $\pi ( \widetilde{X} ) = X$. By virtue of Corollary 9.2.7.13, it will suffice to show that $\widetilde{X}$ is $\widetilde{f}$-local for every morphism $\widetilde{f}$ of $\operatorname{\mathcal{C}}_{/Y}$ satisfying $\pi ( \widetilde{f} ) = f$. This is a special case of Example 9.2.1.2, since $\widetilde{f}$ is an isomorphism (Proposition 4.4.2.11). $\square$