Lemma 6.2.3.1. Let $\operatorname{\mathcal{E}}$ be an $\infty $-category equipped with a functor $U: \operatorname{\mathcal{E}}\rightarrow \Delta ^1$, having fibers $\operatorname{\mathcal{E}}_0 = \{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{E}}$ and $\operatorname{\mathcal{E}}_1 = \{ 1\} \times _{\Delta ^1} \operatorname{\mathcal{E}}$. Let $f: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{E}}$. Then:
The morphism $f$ exhibits $X$ as a $\operatorname{\mathcal{E}}_0$-coreflection of $Y$ (in the sense of Definition 6.2.2.1) if and only if $X$ belongs to $\operatorname{\mathcal{E}}_0$ and $f$ is $\pi $-cartesian.
The morphism $f$ exhibits $Y$ as a $\operatorname{\mathcal{E}}_1$-reflection of $X$ if and only if $Y$ belongs to $\operatorname{\mathcal{E}}_1$ and $f$ is $\pi $-cocartesian.