Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

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.