The Stacks project

Example 14.33.3. Let $\mathcal{C}$, $Y$, $d$, $s$ be as in Example 14.33.1 satisfying the equations of Lemma 14.33.2. Given functors $F : \mathcal{A} \to \mathcal{C}$ and $G : \mathcal{C} \to \mathcal{B}$ we obtain a simplicial object $G \circ X \circ F$ in the category of functors from $\mathcal{A}$ to $\mathcal{B}$ which comes with an augmentation to $G \circ F$.