Remark 8.1.9.4. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of $\infty $-categories and let $W$ be the collection of all $U$-cocartesian morphisms of $\operatorname{\mathcal{E}}$. It follows from Proposition 8.1.9.1 that $U$ also induces an inner fibration $\operatorname{Cospan}^{W, \mathrm{all}}(\operatorname{\mathcal{E}}) \rightarrow \operatorname{Cospan}(\operatorname{\mathcal{C}})$, whose fiber over an object $C \in \operatorname{\mathcal{C}}$ is equivalent to the opposite of the $\infty $-category $\operatorname{\mathcal{E}}_{C}$ (see Variant 8.1.7.14). This construction will play an important role in ยง8.6.
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