Kerodon

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

Example 4.6.6.8. Let $X$ be a Kan complex, which we regard as an object of the $\infty $-category $\operatorname{\mathcal{S}}$ of spaces (Construction 5.6.1.1). Then:

  • The Kan complex $X$ is an initial object of the $\infty $-category $\operatorname{\mathcal{S}}$ if and only if it is empty.

  • The Kan complex $X$ is a final object of the $\infty $-category $\operatorname{\mathcal{S}}$ if and only if it is contractible.