ScalingStacks

Proposition 11.1. If $W$ is a Segal space and $n\geq 3$, the map $\Map_{s{\operatorname{\mathcal{S}}}}(E^{(n)},W)\rightarrow W_{1}$ factors through the subspace $W_{\hoequiv}\subseteq W_{1}$, and induces a weak equivalence $\Map_{s{\operatorname{\mathcal{S}}}}(E^{(n)},W)\rightarrow W_{\hoequiv}$.