ScalingStacks

The equivalence \(\mathcal P^{\Sigma}\colon \mathrm{Cat}_{\infty}^{\sqcup, \mathrm{idem}}\rightarrow\mathrm{Pr}^{\mathrm{L},\mathrm{cp}}\) restricts to an equivalence between full subcategories \[\mathcal P^{\Sigma}\colon\mathrm{add}\xrightarrow{\simeq} \mathrm{Pr}^{\mathrm{L}, \mathrm{cp}}_{\mathrm{add}}.\] Its inverse is \((-)^{\mathrm{cp}}\) which takes a projectively generated additive presentable \(\infty\)-category \(\mathcal C\) to its full subcategory \(\mathcal C^{\mathrm{cp}}\) on the compact-projective objects.