Corollary 7.7.5.10. Small colimits are strongly universal in the $\infty $-category $\operatorname{\mathcal{S}}$.
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Proof. By virtue of Example 7.7.5.3, the $\infty $-category $\operatorname{\mathcal{S}}$ satisfies both Mather cube theorems. Consequently, to show that small colimits in $\operatorname{\mathcal{S}}$ are strongly universal, it will suffice to show that small coproducts in $\operatorname{\mathcal{S}}$ are universal (Corollary 7.7.5.9). This follows from Corollary 7.7.4.12. $\square$