Corollary 5.6.7.6. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Then $U$ is exponentiable (Definition 4.5.9.10). In particular, for any pullback diagram of simplicial sets
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\begin{equation} \begin{gathered}\label{equation:pullback-cocartesian-fibration} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}\ar [r]^-{F} \ar [d]^{U'} & \operatorname{\mathcal{E}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}' \ar [r]^-{\overline{F}} & \operatorname{\mathcal{C}}, } \end{gathered} \end{equation}
if $\overline{F}$ is a categorical equivalence, then $F$ is also a categorical equivalence.