ScalingStacks

Let

$$M\colon\mathrm{N}((\Cat_{\mathcal{S}})^{\mathrm{c}})[W^{-1}]\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{N}((\Cat_{\mathcal{S}})^{\mathrm{c}})[W^{-1}]$$

denote the composite functor

(4.12)

As the previous proposition suggests, $M{\mathcal{A}}$ is essentially the same as the pretriangulated spectral closure $\widehat{{\mathcal{A}}}_{\tri}$ of ${\mathcal{A}}$.