Remark 9.1.3.10. In the situation of Proposition 9.1.3.8, suppose that $\kappa = \aleph _0$. In this case, it suffices to verify conditions $(2)$ and $(3)$ in the special case where $K$ has the form $\operatorname{\partial \Delta }^ n$, for some integer $n \geq 0$. See Lemma 9.1.2.12.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$