Applying proposition 3.1.8.([0033]) and ([0035]) to the full subcategory inclusion \(\mathrm{Sp}_{\geq 0}\rightarrow\mathrm{Sp}\) in \(\mathrm{CAlg}(\mathrm{Pr}^{\mathrm{L},\mathrm{c}})\) and to the subcategory inclusion \(\mathrm{Pr}^{\mathrm{L},\mathrm{cp}}\rightarrow\mathrm{Pr}^{\mathrm{L},\mathrm{c}}\) in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\) (see proposition 3.2.10), we construct the following composite morphism in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\): \[\mathrm{Pr}^{\mathrm{L}, \mathrm{cp}}_{\mathrm{add}}\simeq \mathrm{Mod}_{\mathrm{Sp}_{\geq 0}}(\mathrm{Pr}^{\mathrm{L},\mathrm{cp}}) \xrightarrow{\mathrm{Mod}_{\mathrm{Sp}_{\geq 0}}\left( \mathrm{Pr}^{\mathrm{L},\mathrm{cp}}\rightarrow\mathrm{Pr}^{\mathrm{L},\mathrm{c}}\right)} \mathrm{Mod}_{\mathrm{Sp}_{\geq 0}}(\mathrm{Pr}^{\mathrm{L},\mathrm{c}}) \xrightarrow{-\otimes_{\mathrm{Sp}_{\geq 0}} \mathrm{Sp}} \mathrm{Mod}_{\mathrm{Sp}}(\mathrm{Pr}^{\mathrm{L},\mathrm{c}}) \simeq \mathrm{Pr}^{\mathrm{L}, \mathrm{c}}_{\mathrm{st}}\]
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2