Proposition 7.7.6.6. Let $\lambda $ be an uncountable cardinal, let $\kappa = \mathrm{cf}(\lambda )$ be its cofinality, and let $\operatorname{\mathcal{C}}$ be a $\kappa $-small simplicial set. Then every colimit diagram $\overline{\mathscr {F}}: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{\mathcal{S}}^{< \lambda }$ is strongly universal.
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