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Suppose $\cal{C}$ is a small stable $\infty$-category. Then, we have its K-theory spectrum $K(\cal{C})$ that gives us K-theory groups $K_n(\cal{C})$ by taking stable homotopy groups. There are criteria relating the vanishing of $K_{-1}(\cal{C})$ to the existence of t-structures on $\cal{C}$. Are there "easy-to-use" criteria for the vanishing of $K_1(\cal{C})$?

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