Example 9.2.6.7. Let $\kappa $ be an uncountable regular cardinal. An $\infty $-category $\operatorname{\mathcal{C}}$ is $(\kappa ,\kappa )$-compactly generated if and only if it is idempotent complete (see Example 9.2.2.15). If $\kappa = \aleph _0$, every $\infty $-category is $(\kappa ,\kappa )$-compactly generated.
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