Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 9.1.5.13. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a morphism $g: X \rightarrow Y$. Then every isomorphism $f$ of $\operatorname{\mathcal{C}}$ is weakly left orthogonal to $g$. This follows from the criterion of Remark 9.1.5.12, since every lift of $f$ to the $\infty $-category $\operatorname{\mathcal{C}}_{/Y}$ is also an isomorphism (Proposition 4.4.2.11).