ScalingStacks

Theorem 6.2. If $W$ is a Segal space, then $\Map_{s{\operatorname{\mathcal{S}}}}(E,W)\rightarrow W_{1}$ factors through $W_{\hoequiv}\subseteq W_{1}$, and induces a weak equivalence $\Map_{s{\operatorname{\mathcal{S}}}}(E,W)\rightarrow W_{\hoequiv}$.