Warning 9.2.9.9. Corollary 9.2.9.8 is not quite true in the case $\kappa = \lambda = \aleph _0$: in this case, an object of $\operatorname{Ind}(\operatorname{\mathcal{C}})$ is compact if and only if can be obtained as a retract of an object of $\operatorname{Ind}^{\lambda }_{\kappa }(\operatorname{\mathcal{C}}) \simeq \operatorname{\mathcal{C}}$ (see Proposition 9.2.6.13).
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