Warning 8.6.1.2 (Symmetry). Let $\operatorname{\mathcal{C}}$ be a simplicial set, let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration, and let $U^{\dagger }: \operatorname{\mathcal{E}}^{\dagger } \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$ be a cartesian fibration. In ยง8.6.6, we will show that $U^{\dagger }$ is a cartesian conjugate of $U$ if and only if $U^{\operatorname{op}}$ is a cocartesian conjugate of $U^{\dagger ,\operatorname{op}}$ (Corollary 8.6.6.2). Beware that this is not obvious from Definition 8.6.1.1.
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