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

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

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

Proof. Omitted. $\square$

Comment #1012 by correction_bot on

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

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