Lemma 14.19.13 (018D)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 14: Simplicial Methods
Section 14.19: Coskeleton functors
Lemma 14.19.13 (cite)

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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. $\square$

Comments (2)

Comment #4305 by David Roberts on July 14, 2019 at 00:56

The right hand side has U,V and W mixed up.

Comment #4466 by Johan on September 01, 2019 at 17:08

Thanks and fixed here.

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