Kerodon

Notation 9.4.7.11. Following the convention of Remark 4.9.0.4, an $\infty $-category is essentially small if it is essentially $ \Omega $-small, where $ \Omega $ denotes some fixed strongly inaccessible cardinal. In this case, every accessible $\infty $-category $\operatorname{\mathcal{C}}$ is essentially $ \Omega ^{+}$-small (Remark 9.4.6.14). We let $\operatorname{\mathcal{QC}}^{\operatorname{Acc}}$ denote the subcategory of $\operatorname{\mathcal{QC}}_{\leq \Omega }$ whose objects are accessible $\infty $-categories and whose morphisms are accessible functors. We will refer to $\operatorname{\mathcal{QC}}^{\operatorname{Acc}}$ as the $\infty $-category of accessible $\infty $-categories.