Example 5.3.7.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Applying Corollary 5.3.7.3 in the case where both $F$ and $G$ are the identity functor $\operatorname{id}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}$, we deduce that the evaluation functor
\[ \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( \{ 0\} , \operatorname{\mathcal{C}}) \simeq \operatorname{\mathcal{C}} \]
is a cartesian fibration of $\infty $-categories, and the evaluation functor
\[ \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( \{ 1\} , \operatorname{\mathcal{C}}) \simeq \operatorname{\mathcal{C}} \]
is a cocartesian fibration of $\infty $-categories.