Remark 6.3.6.7. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [r] \ar [d]^{f'} & X \ar [d]^{f} \\ S' \ar [r] & S. } \]
If $f$ is universally localizing, then $f'$ is universally localizing.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$