ScalingStacks

Proof. That this map is a weak equivalence from each component of $\class({\operatorname{\mathcal{S}}}^{I})$ to the corresponding component of the homotopy limit follows from [DK84a, 3.4(iii)]. That the map is surjective on path components is a consequence of Proposition 3.4 and Theorem 3.7 of [DK84b]. ∎