ScalingStacks

The equivalence \(\operatorname{Ind}\colon \mathrm{Cat}_{\infty}^{\mathrm{rex}, \mathrm{idem}}\rightarrow\mathrm{Pr}^{\mathrm{L},\mathrm{c}}\) restricts to an equivalence between full subcategories \[\operatorname{Ind}\colon\mathrm{st}\xrightarrow{\simeq}\mathrm{Pr}^{\mathrm{L}, \mathrm{c}}_{\mathrm{st}}.\] Its inverse is \((-)^{\mathrm{c}}\) which takes a compactly generated stable presentable \(\infty\)-category \(\mathcal C\) to its full subcategory \(\mathcal C^{\mathrm{c}}\) on the compact objects.