Kerodon

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Proposition 5.1.4.12. Let $q: X \rightarrow S$ be a cartesian fibration of simplicial sets and let $\sigma : \Delta ^2 \rightarrow X$ be a $2$-simplex of $X$, which we will depict as a diagram

$\xymatrix@R =50pt@C=50pt{ & y \ar [dr]^{g} & \\ x \ar [ur]^{f} \ar [rr]^{h} & & z. }$

Suppose that $g$ is $q$-cartesian. Then $f$ is $q$-cartesian if and only if $h$ is $q$-cartesian.