Kerodon

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

Corollary 5.2.4.6. Suppose we are given a commutative diagram of simplicial sets

\[ \xymatrix@R =50pt@C=50pt{ X \ar [r] \ar [d] & Y \ar [d] \\ X' \ar [r] & Y', } \]

where the vertical maps are categorical equivalences. Then the induced map $X \star _{Y} Y \rightarrow X' \star _{Y'} Y'$ is also a categorical equivalence of simplicial sets.