Kerodon

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

Corollary 4.5.2.23. Suppose we are given a pullback diagram of $\infty $-categories

\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}' \ar [r]^-{F'} \ar [d] & \operatorname{\mathcal{C}}\ar [d]^{U} \\ \operatorname{\mathcal{D}}' \ar [r]^-{F} & \operatorname{\mathcal{D}}, } \]

where $U$ is an isofibration. If $F$ is an equivalence of $\infty $-categories, then $F'$ is also an equivalence of $\infty $-categories.