Lemma 14.19.13. Assume $\mathcal{C}$ has fibre products. Let $U \to V$ and $W \to V$ be morphisms of $n$-truncated simplicial objects of the category $\mathcal{C}$. Then
\[ \text{cosk}_ n (U \times _ V W) = \text{cosk}_ nU \times _{\text{cosk}_ n V} \text{cosk}_ nW \]
whenever the left and right hand side exist.
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