ScalingStacks

Corollary 4.27. Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be idempotent-complete small stable $\infty$-categories and let $\Upsilon(A)$ and $\Upsilon(B)$ be spectral categories lifting ${\mathcal{A}}$ and ${\mathcal{B}}$. Then $\mathrm{N}(\mathrm{rep}({\mathcal{A}},{\mathcal{B}}))\simeq\mathrm{Fun}^{\ex}\!({\mathcal{A}},\!{\mathcal{B}})$ is equivalent to the $\infty$-category of right-compact $\Upsilon(A)^{\op}\wedge\Upsilon(B)$-modules.