# Kerodon

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

Example 5.2.4.4. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be morphisms of simplicial sets. If $\operatorname{\mathcal{D}}$ is empty, then the inclusion map $\iota _{\operatorname{\mathcal{C}}}: \operatorname{\mathcal{C}}\hookrightarrow \operatorname{\mathcal{C}}\star _{\operatorname{\mathcal{E}}} \operatorname{\mathcal{D}}$ is an isomorphism of simplicial sets. If $\operatorname{\mathcal{C}}$ is empty, then the inclusion map $\iota _{\operatorname{\mathcal{D}}}: \operatorname{\mathcal{D}}\hookrightarrow \operatorname{\mathcal{C}}\star _{\operatorname{\mathcal{E}}} \operatorname{\mathcal{D}}$ is an isomorphism of simplicial sets.