Kerodon

Proposition 9.4.1.3. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of $\infty $-categories and let $\mathbb {K}$ be a collection of simplicial sets. Then $U$ is $\mathbb {K}$-cocomplete if and only if, for every morphism $\Delta ^1 \rightarrow \operatorname{\mathcal{C}}$, the inner fibration $\Delta ^1 \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}\rightarrow \Delta ^1$ is $\mathbb {K}$-cocomplete.