# Kerodon

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

Remark 4.1.1.4. The collection of inner fibrations is closed under retracts. That is, given a diagram of simplicial sets

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

where both horizontal compositions are the identity, if $q'$ is an inner fibration, then so is $q$.