Lemma 6.47.
Let \(U \in T\) be an \(\infty\)-connected object. Then the constant simplicial object with value \(U\) is a hypercover in \(T\).
Proof
By Corollary 6.46, we may assume that \(T\) is hypercomplete. Then \(U \simeq *\), so the constant simplicial object with value \(U\) is the terminal object of \(\Fun(\simp\catop, T)\). Since the coskeleton functors preserve limits, the matching maps are all isomorphisms.