ScalingStacks

Remark 4.3. Using the machinery of combinatorial simplicial model categories, we can also localize the combinatorial model structure of corollary 2.4 on $\Cat_{\mathcal{S}}$ at the triangulated or Morita equivalences directly to obtain “triangulated” or “Morita” simplicial model categories on small spectral categories and then pass to simplicial nerves; this is equivalent to localizing the $\infty$-category $\mathrm{N}((\Cat_{\mathcal{S}})^{\cf})$.