Still in the setup of example 3.5.15, the \(\infty\)-categories \(\left(\mathrm{Mod}_{Hk}^{\geq 0, Z}\right)^{\mathrm{cp}}\) and \(\left(\mathrm{Mod}_{Hk}^{Z}\right)^{\mathrm{c}}\) may be identified with the full subcategories \(\mathrm{Fun}^{\mathrm{fin.supp.}}(Z, \mathrm{CProj}_{k})\) and \(\mathrm{Fun}^{\mathrm{fin.supp.}}(Z, \mathrm{Perf}_{k})\) of the functor \(\infty\)-categories \(\mathrm{Fun}(Z, \mathrm{CProj}_{k})\) and \(\mathrm{Fun}(Z, \mathrm{Perf}_{k})\), respectively, on the finitely supported functors, i.e. functors that vanish on all but finitely many elements of \(Z\).
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2