ScalingStacks

Proof. This is follows from the fact that $i_{!}\colon\Psi(F_{R})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\Psi(F^{\infty}_{R})$ is fully faithful, which in turn follows from the fact that $i$ is a fully faithful functor of spectral categories. ∎