# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 5.3.7.2. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. Applying Proposition 5.3.7.1 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.