ScalingStacks

Theorem 4.22. The functor

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

admits a fully faithful and accessible right adjoint

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

That is, the $\infty$-category of stable $\infty$-categories is an accessible localization of the $\infty$-category of spectral categories obtained by inverting the triangulated equivalences.