Exercise 1.1.3.7. Show that the inequality of Proposition 1.1.3.6 is sharp. That is, if $S^{-}$ and $S^{+}$ are nonempty simplicial sets of dimensions $k_{-}$ and $k_{+}$, respectively, then the product $S^{-} \times S^{+}$ has dimension $k_{-} + k_{+}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$