ScalingStacks

Remark 9.33. On $0$-connective covers there is an equivalence $K({\mathcal{C}})_{>0}\simeq I\mspace{-6.mu}K({\mathcal{C}})_{>0}$ between this notion of non-connective $K$-theory and the usual connective $K$-theory of ${\mathcal{C}}$. In degree $0$, there an isomorphism $\pi_{0}K({\mathcal{C}})\cong\pi_{0}I\mspace{-6.mu}K({\mathcal{C}})$ if the underlying $\infty$-category of ${\mathcal{C}}$ is idempotent complete.