Free Duals and a New Universal Property for Stable Equivariant Homotopy Theory

In this thesis, I study the left adjoint D to the forgetful functor from the ∞-category of symmetric monoidal ∞-categories with duals and finite colimits to the ∞-category of symmetric monoidal ∞-categories with finite colimits, and related free constructions. My main result is that D(C) always splits as the product of 3 factors, each characterized by a certain universal property. As an application, I show that, for any compact Lie group G, the ∞-category of genuine G-spectra is obtained from the ∞-category of naive G-spectra by freely adjoining duals for compact objects, while respecting colimits.