Example 11.3.0.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing an object $X$. Then the left fibrations
\[ \operatorname{\mathcal{C}}_{X/} \rightarrow \operatorname{\mathcal{C}}\quad \quad \{ X\} \operatorname{\vec{\times }}_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}} \]
are corepresentable by $X$, and the right fibrations
\[ \operatorname{\mathcal{C}}_{/X} \rightarrow \operatorname{\mathcal{C}}\quad \quad \operatorname{\mathcal{C}}\operatorname{\vec{\times }}_{\operatorname{\mathcal{C}}} \{ X\} \rightarrow \operatorname{\mathcal{C}} \]
are representable by $X$. See Proposition 4.6.7.22.