Example 7.7.5.4. Let $\operatorname{\mathcal{C}}$ be (the nerve of) the category of sets. Then $\operatorname{\mathcal{C}}$ satisfies the second Mather cube theorem (Exercise 3.4.3.1), but does not satisfy the first Mather cube theorem (Warning 3.4.4.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$