Kerodon

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

Example 5.2.4.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be simplicial sets, so that we have unique morphisms $F: \operatorname{\mathcal{C}}\rightarrow \Delta ^{0}$ and $G: \operatorname{\mathcal{D}}\rightarrow \Delta ^{0}$. Then the relative join $\operatorname{\mathcal{C}}\star _{\Delta ^{0}} \operatorname{\mathcal{D}}$ agrees with the join $\operatorname{\mathcal{C}}\star \operatorname{\mathcal{D}}$ introduced in Construction 4.3.3.13.