Kerodon

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

Exercise 1.1.3.12. Show that the inequality of Proposition 1.1.3.11 is sharp. That is, if $S_{\bullet }^{-}$ and $S_{\bullet }^{+}$ are nonempty simplicial sets of dimensions $k_{-}$ and $k_{+}$, respectively, then the product $S_{\bullet }^{-} \times S_{\bullet }^{+}$ has dimension $k_{-} + k_{+}$.