Remark 9.2.3.7. In the situation of Proposition 9.2.3.6, a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves $\kappa $-sequential colimits (in the sense of Definition 9.2.3.1) if and only if it is $(\kappa , \kappa ^{+})$-finitary (in the sense of Definition 9.2.2.6). In other words, we have an equality $\operatorname{\mathcal{QC}}^{\kappa -\mathrm{seq}} = \operatorname{\mathcal{QC}}^{ (\kappa ,\kappa ^{+} )-\mathrm{ccomp} }$ of subcategories of $\operatorname{\mathcal{QC}}$ (see Notations 9.2.3.4 and 9.2.2.14).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$