Proposition 7.2.8.7. Every sifted simplicial set is weakly contractible.
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Proposition 7.2.8.7. Every sifted simplicial set is weakly contractible.
Proof. Let $K$ be a sifted simplicial set. Taking $I = \emptyset $ in Definition 7.2.8.1, we conclude that the projection map $K \rightarrow \Delta ^0$ is right cofinal, so that $K$ is weakly contractible by virtue of Proposition 7.2.1.5. $\square$