Example 11.5.0.86. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing objects $X$ and $Y$. The following conditions are equivalent:
The objects $X$ and $Y$ are isomorphic.
The object $Y$ is a limit of the diagram $\{ X \} \hookrightarrow \operatorname{\mathcal{C}}$.
The object $Y$ is a colimit of the diagram $\{ X\} \hookrightarrow \operatorname{\mathcal{C}}$.
See Example 7.1.1.5 for a more precise statement.