Remark 9.3.1.11. In the formulation of Remark 9.3.1.10, we can replace $\operatorname{\partial \Delta }^{n+2}$ by any simplicial set $K$ of the same weak homotopy type (that is, any simplicial set $K$ for which the geometric realization $|K|$ is homotopy equivalent to a sphere of dimension $n+1$). For example, we can take $K$ to be the subdivision $\operatorname{Sd}( \Delta ^{n+1} )$ (see Proposition 3.3.4.8).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$