ScalingStacks

Corollary 4.16. The functor $\eta_{{\mathcal{A}}}\colon{\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}M{\mathcal{A}}$ is an equivalence of spectral categories if and only if ${\mathcal{A}}$ is a stable spectral category.