Kerodon

Remark 9.2.6.6. Following the convention of Remark 4.7.0.5, a regular cardinal $\kappa $ is small if it satisfies $\kappa < \operatorname{\textnormal{\cjRL {t}}}$, for some fixed strongly inaccessible cardinal $\operatorname{\textnormal{\cjRL {t}}}$. In this case, an $\infty $-category $\operatorname{\mathcal{C}}$ is $\kappa $-compactly generated (in the sense of Definition 9.2.6.3) if and only if it is $(\kappa ,\operatorname{\textnormal{\cjRL {t}}})$-compactly generated (in the sense of Variant 9.2.6.5). In particular, $\operatorname{\mathcal{C}}$ is compactly generated if and only if it is $(\aleph _0, \operatorname{\textnormal{\cjRL {t}}})$-compactly generated. See Remark 9.2.2.14.