Kerodon

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Example 9.5.0.34. 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.