Example 7.1.10.6. Let $B$ and $K$ be simplicial sets, and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits $K$-indexed colimits. Applying Corollary 7.1.10.5 to the cartesian fibration $U: \operatorname{\mathcal{C}}\times B \rightarrow B$, we recover the assertion that the $\infty $-category
\[ \operatorname{Fun}( B, \operatorname{\mathcal{C}}) \simeq \operatorname{Fun}_{ / B}(B, \operatorname{\mathcal{C}}\times B ) \]
admits $K$-indexed colimits, which are computed levelwise (see Proposition 7.1.8.2).