ScalingStacks

Proof: In Lemma 3.3, $\text{Hom}(S,{\mathrm{\Sigma }}^i\mu ):\text{Hom}(S,{\mathrm{\Sigma }}^i{M}_k)\to \text{Hom}(S,{\mathrm{\Sigma }}^i{M}_{k+1})$ is an isomorphism for . Now apply Lemma 4.2. $\mathrm{\square }$