Remark 4.6.8.31. It follows from Lemma 4.6.8.30 that the morphism $\pi $ of Construction 4.6.8.29 induces an isomorphism of simplicial sets $\Delta ^{0} \diamond \Phi (\Delta ^ n) \rightarrow \Phi ( \Delta ^{n+1} )$, where $\diamond $ denotes the blunt join of Notation 4.5.8.3.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$