ScalingStacks

As \(\mathrm{Sp}_{\geq 0}\) is an idempotent algebra in \(\mathrm{Pr}^\mathrm{L}\), the second functor \(-\otimes_{\mathrm{Sp}_{\geq 0}} \mathrm{Sp}\) here is equivalent to the composite \[ \mathrm{Mod}_{\mathrm{Sp}_{\geq 0}}(\mathrm{Pr}^{\mathrm{L},\mathrm{c}}) \xrightarrow{\mathrm{forget}} \mathrm{Pr}^{\mathrm{L},\mathrm{c}}\xrightarrow{-\otimes \mathrm{Sp}} \mathrm{Mod}_{\mathrm{Sp}}(\mathrm{Pr}^{\mathrm{L},\mathrm{c}}).\]