# Kerodon

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Remark 1.1.4.3. Let $C$ be an object of the category $\operatorname{\mathcal{C}}$. The constant simplicial object $\underline{C}_{\bullet }$ can be described concretely as follows:

• For each $n \geq 0$, we have $\underline{C}_{n} = C$.

• The face and degeneracy operators

$d_{i}: \underline{C}_{n} \rightarrow \underline{C}_{n-1} \quad \quad s_{i}: \underline{C}_{n} \rightarrow \underline{C}_{n+1}$

are the identity maps from $C$ to itself.