The Stacks project

Remark 14.20.4. Let $\mathcal{C}$ be a category with fibre products. Let $V$ be a simplicial object. Let $\epsilon : V \to X$ be an augmentation. Let $U$ be the simplicial object whose $n$th term is the $(n + 1)$st fibred product of $V_0$ over $X$. By a simple combination of Lemmas 14.20.2 and 14.20.3 we obtain a canonical morphism $V \to U$.