ScalingStacks

Theorem 1.11. (see theorem 3.7) An idempotent-complete small stable $\infty$-category ${\mathcal{A}}$ is dualizable (as an object of the symmetric monoidal $\infty$-category $\Cat_{\infty}^{\perf}$) if and only if ${\mathcal{A}}$ is smooth and proper. Moreover, the dual of a dualizable idempotent-complete small stable $\infty$-category ${\mathcal{A}}$ is the opposite $\infty$-category ${\mathcal{A}}^{\op}$.