Kerodon

Example 5.2.3.7. Let $\operatorname{\mathcal{E}}$ be a simplicial set equipped with a morphism $\pi : \operatorname{\mathcal{E}}\rightarrow \Delta ^1$, and set $\operatorname{\mathcal{C}}= \{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{E}}$ and $\operatorname{\mathcal{D}}= \{ 1\} \times _{\Delta ^1} \operatorname{\mathcal{E}}$. Then the relative join $\operatorname{\mathcal{C}}\star _{\operatorname{\mathcal{E}}} \operatorname{\mathcal{D}}$ is isomorphic to $\operatorname{\mathcal{E}}$.