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

whenever the left and right hand side exist.

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.

**Proof.**
Omitted, but very similar to the proof of Lemma 14.19.12 above.
$\square$

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## Comments (2)

Comment #4305 by David Roberts on

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