Corollary 7.7.3.20. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is locally cartesian closed. Then every weak colimit diagram $K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a descent diagram for the evaluation functor $\operatorname{ev}_1: \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. By virtue of Corollary 7.7.2.33, it will suffice to show that for every morphism $f: X \rightarrow Y$ of $\operatorname{\mathcal{C}}$, the pullback functor $f^{\ast }: \operatorname{\mathcal{C}}_{/Y} \rightarrow \operatorname{\mathcal{C}}_{/X}$ preserves $K$-indexed colimits. This follows from Corollary 7.1.4.22, since the functor $f^{\ast }$ has a right adjoint (Proposition 7.7.3.19). $\square$