Lemma 14.7.2 (016U)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 14: Simplicial Methods
Section 14.7: Fibre products of simplicial objects
Lemma 14.7.2 (cite)

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Lemma 14.7.2. If $U, V, W$ are simplicial objects in the category $\mathcal{C}$ , and if $a : V \to U$ , $b : W \to U$ are morphisms and if $V \times _ U W$ exists, then we have

$\mathop{\mathrm{Mor}}\nolimits (T, V \times _ U W) = \mathop{\mathrm{Mor}}\nolimits (T, V) \times _{\mathop{\mathrm{Mor}}\nolimits (T, U)} \mathop{\mathrm{Mor}}\nolimits (T, W)$

for any fourth simplicial object $T$ of $\mathcal{C}$ .

Proof. Omitted. $\square$

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Comment #1012 by correction_bot on September 09, 2014 at 03:39

In $\Mor(T, V \times_U V)$ , replace $V \times_U V$ with $V \times_U W$

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