Kerodon

Variant 9.2.9.5. Let $\kappa $ be a regular cardinal and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of simplicial sets. We say that $U$ is $\kappa $-sequentially cocomplete if, for every $n$-simplex $\sigma : \Delta ^ n \rightarrow \operatorname{\mathcal{C}}$, the fiber product $\operatorname{\mathcal{E}}_{\sigma } = \Delta ^ n \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is a $\kappa $-sequentially cocomplete $\infty $-category (Definition 9.2.3.1). In other words, the inner fibration $U$ is $\kappa $-sequentially cocomplete if and only if it is $(\kappa , \kappa ^{+})$-cocomplete (in the sense of Definition 9.2.9.4); see Proposition 9.2.3.6.