ScalingStacks

Corollary 7.9. Let ${\mathcal{C}}$ be a small pretriangulated spectral category and let ${\mathcal{M}}_{{\mathcal{C}}}$ denote the category of perfect ${\mathcal{C}}$-modules with its Waldhausen structure induced by the model structure on ${\mathcal{C}}$-modules. Then there is an isomorphism in the stable category

$$K({\mathcal{M}}_{{\mathcal{C}}})\simeq K(\Psi_{\perf}{\mathcal{C}}).$$