Variant 5.5.5.9. Let $\kappa $ be an uncountable cardinal. We let $\operatorname{ \pmb {\mathcal{QC}} }^{< \kappa }$ denote the full simplicial subset of $\operatorname{ \pmb {\mathcal{QC}} }$ spanned by those $\infty $-categories $\operatorname{\mathcal{C}}$ which are $\kappa $-small. Then $\operatorname{ \pmb {\mathcal{QC}} }^{< \kappa }$ is an $(\infty ,2)$-category, which we will refer to as the $(\infty ,2)$-category of essentially $\kappa $-small $\infty $-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$