Warning 8.6.2.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. If $\operatorname{\mathcal{C}}$ is not an $\infty $-category, then the morphism $V: \operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( \operatorname{Tw}(\operatorname{\mathcal{C}}) / \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$ given by Construction 8.6.2.2 need not be a cartesian conjugate of $U$. In ยง8.6.3, we will give an alternative construction of a cartesian conjugate which works in complete generality (Proposition 8.6.3.5).
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