Proposition 9.2.7.8. Let $X$ be a Kan complex. Then $X$ finitely dominated if and only if it is compact when viewed as an object of the $\infty $-category $\operatorname{\mathcal{S}}$.
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Proposition 9.2.7.8. Let $X$ be a Kan complex. Then $X$ finitely dominated if and only if it is compact when viewed as an object of the $\infty $-category $\operatorname{\mathcal{S}}$.
Proof. Combine Corollary 9.2.7.6 with Proposition 9.2.6.13. $\square$