Remark 8.6.3.2. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Low-dimensional simplices of the simplicial set $\operatorname{Cospan}^{\dagger }(\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}})$ can be described as follows:
Vertices of the simplicial set $\operatorname{Cospan}^{\dagger }(\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}})$ can be identified with vertices of the simplicial set $\operatorname{\mathcal{E}}$.
Let $X$ and $Y$ be vertices of $\operatorname{Cospan}^{\dagger }(\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}})$. Then edges $e: X \rightarrow Y$ of $\operatorname{Cospan}(\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}})$ can be identified with pairs of edges $X \xrightarrow {f} B \xleftarrow {g} Y$ in the simplicial set $\operatorname{\mathcal{E}}$ having the property that $g$ is $U$-cocartesian and $U(f)$ is a degenerate edge of $\operatorname{\mathcal{C}}$.