Kerodon

Remark 9.4.1.9. In condition $(4)$ of Definition 9.4.1.8, we have implicitly assumed that the $\infty $-category $\widehat{\operatorname{\mathcal{E}}}$ is locally small and that each of the simplicial sets $K \in \mathbb {K}$ is (essentially) small. If these conditions are not satisfied, then we should replace the $\infty $-category $\operatorname{\mathcal{S}}$ by $\operatorname{\mathcal{S}}^{< \lambda }$, where $\lambda $ is some regular cardinal having the property that $\widehat{\operatorname{\mathcal{E}}}$ is locally $\tau $-small and each $K \in \mathbb {K}$ is essentially $\tau $-small.