Corollary 5.6.7.8. Suppose we are given a commutative diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{D}}\ar [rr]^-{F} \ar [dr]_{U} & & \operatorname{\mathcal{E}}\ar [dl]^{V} \\ & \operatorname{\mathcal{C}}, & } \]
where $U$ and $V$ are cocartesian fibrations. Then $F$ is an equivalence of cocartesian fibrations over $\operatorname{\mathcal{C}}$ (Definition 5.1.7.1) if and only if it is a categorical equivalence of simplicial sets.