Free duals and a new universal property for stable equivariant homotopy theory

We study the left adjoint $\mathbb{D}$ to the forgetful functor from the $\mathrm{\infty }$-category of symmetric monoidal $\mathrm{\infty }$-categories with duals and finite colimits to the $\mathrm{\infty }$-category of symmetric monoidal $\mathrm{\infty }$-categories with finite colimits, and related free constructions. The main result is that $\mathbb{D}\mathcal{C}$ always splits as the product of 3 factors, each characterized by a certain universal property. As an application, we show that, for any compact Lie group $G$, the $\mathrm{\infty }$-category of genuine $G$-spectra is obtained from the $\mathrm{\infty }$-category of Bredon (\emph{a.k.a} ``naive") $G$-spectra by freely adjoining duals for compact objects, while respecting colimits.