Kerodon

Example 11.3.0.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the left fibration $\operatorname{id}_{\operatorname{\mathcal{C}}}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}$ is corepresentable if and only if $\operatorname{\mathcal{C}}$ has an initial object, and the right fibration $\operatorname{id}_{\operatorname{\mathcal{C}}}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}$ is representable if and only if $\operatorname{\mathcal{C}}$ has a final object.