Kerodon

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

Remark 3.1.1.5. The collection of Kan fibrations is closed under retracts. That is, given a diagram of simplicial sets

\[ \xymatrix@R =50pt@C=50pt{ X_{} \ar [r] \ar [d]^{f} & X'_{} \ar [d]^{f'} \ar [r] & X_{} \ar [d]^{f} \\ S_{} \ar [r] & S'_{} \ar [r] & S_{} } \]

where both horizontal compositions are the identity, if $f'$ is a Kan fibration, then so is $f$.