ScalingStacks

Let \(\mathbb{K}\in \mathrm{CAlg}(\mathrm{Sp})\). The rank one free module \(\mathbb{K}_{\mathbb{K}}\) generates \(\mathrm{Perf}_{\mathbb{K}}\) under retracts and finite colimits; in particular, every object of \(\mathrm{Perf}_{\mathbb{K}}\) is a retract of an iterated finite colimit of modules isomorphic to \(\mathbb{K}_{\mathbb{K}}\).