Together with the symmetric monoidal left adjoint of the forgetful functor \(\mathrm{Cat}_{\infty}^{\mathrm{rex}, \mathrm{idem}}\rightarrow\mathrm{Cat}_{\infty}^{\sqcup, \mathrm{idem}}\) from proposition 3.1.11.([003D]), the symmetric monoidal subcategory inclusion \(\mathrm{Pr}^{\mathrm{L},\mathrm{cp}}\rightarrow\mathrm{Pr}^{\mathrm{L},\mathrm{c}}\) assemble into a commutative diagram in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\): 
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2