ScalingStacks

Proof of (6.2) from (11.1). Since $E$ is the colimit of the $E^{(n)}$ along a sequence of cofibrations, it follows by (11.1) that $\Map_{s{\operatorname{\mathcal{S}}}}(E,W)$ is the inverse limit of the $\Map_{s{\operatorname{\mathcal{S}}}}(E^{(n)},W)$ along a tower of trivial fibrations. The proposition follows. ∎