Definition 7.7.2.6. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cartesian fibration of simplicial sets. We say that a morphism of simplicial sets $F: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a descent diagram for $U$ if the restriction map
\[ \theta : \operatorname{Fun}_{ / \operatorname{\mathcal{C}}}^{\operatorname{ACart}}( K^{\triangleright }, \operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}_{ / \operatorname{\mathcal{C}}}^{\operatorname{ACart}}(K, \operatorname{\mathcal{E}}) \quad \quad \widetilde{F} \mapsto \widetilde{F}|_{K} \]
is fully faithful. We say that $F$ is an effective descent diagram for $U$ if $\theta $ is an equivalence of $\infty $-categories.