Remark 7.7.2.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits pullbacks and let
\[ \operatorname{ev}_{1}: \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}} \]
denote the cartesian fibration given by evaluation at the vertex $1 \in \Delta ^1$. It follows from Notation 7.7.2.10 that a morphism $F: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a descent diagram for $\operatorname{ev}_{1}$ if and only if the restriction functor
\[ \theta : \operatorname{Fun}( K^{\triangleright }, \operatorname{\mathcal{C}})^{\operatorname{Cart}}_{/F} \rightarrow \operatorname{Fun}( K, \operatorname{\mathcal{C}})^{\operatorname{Cart}}_{/F|_{K}} \]
is fully faithful. Similarly $F$ is an effective descent diagram for $\operatorname{ev}_{1}$ if and only if $\theta $ is an equivalence of $\infty $-categories.