The main application of this paper will only be concerned with the case that \(\mathbb{K}= Hk\) is an Eilenberg-MacLane spectrum of a classical commutative ring \(k\). In this case, \(\mathrm{Mod}_{\mathbb{K}}\) is equivalent to the unbounded derived \(\infty\)-category \(\mathcal D(\mathrm{mod}_k)\) of the abelian category \(\mathrm{mod}_k\) of \(k\)-modules [Lur17, Thm 7.1.2.13] with symmetric monoidal structure given by the derived tensor product \(-\otimes^L_k-\). The \(\infty\)-category \(\mathrm{Perf}_{\mathbb{K}}\) is equivalent to its full subcategory on the perfect chain complexes, i.e. the chain complexes quasi-isomorphic to a bounded complex of finitely generated projective \(k\)-modules.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2