Kerodon

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

Example 7.2.1.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $X$ be an object of $\operatorname{\mathcal{C}}$. Then the inclusion map $\{ X\} \hookrightarrow \operatorname{\mathcal{C}}$ is right cofinal if and only if $X$ is a final object of $\operatorname{\mathcal{C}}$. This follows by combining Proposition 7.2.1.3 with Corollary 4.6.6.25. Similarly, the inclusion map $\{ X \} \hookrightarrow \operatorname{\mathcal{C}}$ is left cofinal if and only if $X$ is an initial object of $\operatorname{\mathcal{C}}$.