Every spectrum is the K-theory of a stable $\infty$-category

Abstract

We prove that any spectrum is equivalent to the nonconnective K-theory of a stable $\infty$-category. We use these results to construct a stable $\infty$-category $\mathcal{C}$ with a bounded t-structure such that $K(\mathcal{C})$ is not equivalent to $K({\mathcal{C}}^{♡})$, disproving a conjecture of Antieau, Gepner, and Heller.

17 pages