Example 24.3.4. Let $\{ U_ i \to X\} _{i \in I}$ be a covering of the site $\mathcal{C}$. Set $K_0 = \{ U_ i \to X\} _{i \in I}$. Then $K_0$ is a $0$-truncated simplicial object of $\text{SR}(\mathcal{C}, X)$. Hence we may form

Clearly $K$ passes condition (1) of Definition 24.3.3. Since all the morphisms $K_{n + 1} \to (\text{cosk}_ n \text{sk}_ n K)_{n + 1}$ are isomorphisms by Simplicial, Lemma 14.19.10 it also passes condition (2). Note that the terms $K_ n$ are the usual

## Comments (2)

Comment #1025 by correction_bot on

Comment #1031 by Johan on

There are also: