Kerodon

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

Example 4.4.1.10. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a right fibration between $\infty $-categories. Then $F$ is an inner fibration (Remark 4.2.1.4), and any isomorphism $u: D \rightarrow F(C)$ can be lifted to a morphism $\overline{u}: \overline{D} \rightarrow C$ in $\operatorname{\mathcal{C}}$, which is automatically an isomorphism by virtue of Proposition 4.4.2.9. It follows that $F$ is an isofibration. Similarly, any left fibration of $\infty $-categories is an isofibration. For a more general statement, see Theorem .