Remark 7.7.1.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $K$ be a simplicial set, and suppose we are given a commutative diagram
\[ \xymatrix { & \mathscr {G} \ar [dr]^{\beta } & \\ \mathscr {F} \ar [ur]^{ \alpha } \ar [rr]^{\gamma } & & \mathscr {H} } \]
in the $\infty $-category $\operatorname{Fun}(K, \operatorname{\mathcal{C}})$, where the natural transformation $\beta $ is cartesian. Then $\alpha $ is cartesian if and only if $\gamma $ is cartesian (see Proposition 7.6.2.28). In particular, the collection of cartesian natural transformations is closed under composition in $\operatorname{Fun}(K, \operatorname{\mathcal{C}})$.