Kerodon

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

Example 8.6.4.18. In the special case $\operatorname{\mathcal{C}}= \Delta ^0$, Corollary 8.6.4.17 asserts that every Kan complex $X = \operatorname{\mathcal{E}}$ is homotopy equivalent to the opposite Kan complex $X^{\operatorname{op}}$. This can also be deduced from Theorem 3.6.0.1, since the geometric realizations $|X|$ and $|X^{\operatorname{op}}|$ are homeomorphic.