Notation 1.1.0.5. We will often use an expression like $C_{\bullet }$ to denote a simplicial object of a category $\operatorname{\mathcal{C}}$. In this case, we write $C_{n}$ for the value of the functor $C_{\bullet }$ on the object $[n] \in \operatorname{{\bf \Delta }}$. Similarly, we often use an expression like $C^{\bullet }$ to indicate a cosimplicial object of $\operatorname{\mathcal{C}}$, and $C^{n}$ for its value on $[n] \in \operatorname{{\bf \Delta }}$.
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