Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 8.4.0.5. 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.