Example 8.6.3.12. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of $\infty $-categories. Applying Construction 8.6.3.9 to the evaluation functor
\[ \operatorname{Fun}^{\operatorname{CCart}}_{/\operatorname{\mathcal{C}}}( \operatorname{Tw}(\operatorname{\mathcal{C}}) / \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{E}}) \times _{ \operatorname{\mathcal{C}}^{\operatorname{op}} } \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{E}}\quad \quad (C, f_ C, u: C \rightarrow C') \mapsto f_ C(u), \]
we we obtain a comparison functor
\[ \Psi : \operatorname{Fun}^{\operatorname{CCart}}_{/\operatorname{\mathcal{C}}}( \operatorname{Tw}(\operatorname{\mathcal{C}}) / \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{Cospan}^{\dagger }( \operatorname{\mathcal{E}}/ \operatorname{\mathcal{C}}). \]
It follows from Propositions 8.6.3.11 and 8.6.2.3 that this functor is an equivalence of $\infty $-categories.