Example 8.1.3.3. Let $\operatorname{\mathcal{C}}$ be a simplicial set. Then:
Vertices of the simplicial set $\operatorname{Cospan}(\operatorname{\mathcal{C}})$ can be identified with vertices of $\operatorname{\mathcal{C}}$.
Let $X$ and $Y$ be vertices of $\operatorname{\mathcal{C}}$. Then edges of $\operatorname{Cospan}(\operatorname{\mathcal{C}})$ joining $X$ to $Y$ can be identified with pairs $(f,g)$, where $f: X \rightarrow B$ and $g: Y \rightarrow B$ are edges of $\operatorname{\mathcal{C}}$ having the same target.