Kerodon

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

Remark 5.1.1.10. Suppose we are given a pullback diagram of simplicial sets

\[ \xymatrix@R =50pt@C=50pt{ X' \ar [d]^-{q'} \ar [r]^-{f} & X \ar [d]^-{q} \\ S' \ar [r] & S. } \]

Let $e'$ be an edge of the simplicial set $X'$, having image $e = f(e')$ in $X$. If $e$ is $q$-cartesian, then $e'$ is $q'$-cartesian. Similarly, if $e$ is $q$-cocartesian, then $e'$ is $q'$-cocartesian.