Remark 9.4.2.5. Following the convention of Remark 4.9.0.4, a regular cardinal $\kappa $ is small if it satisfies $\kappa < \Omega $, where $ \Omega $ is some fixed strongly inaccessible cardinal. In this case, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\kappa $-compact (in the sense of Variant 9.4.2.2) if and only if it is $(\kappa , \Omega )$-compact (in the sense of Variant 9.4.2.4).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$