# Kerodon

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

Corollary 6.2.3.2. Let $\operatorname{\mathcal{E}}$ be an $\infty$-category equipped with a functor $U: \operatorname{\mathcal{E}}\rightarrow \Delta ^1$. Then:

• The functor $U$ is a cartesian fibration if and only if the full subcategory $\{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{E}}\subseteq \operatorname{\mathcal{E}}$ is coreflective.

• The functor $U$ is a cocartesian fibration if and only if the full subcategory $\{ 1\} \times _{\Delta ^1} \operatorname{\mathcal{E}}\subseteq \operatorname{\mathcal{E}}$ is reflective.