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

<p>In this thesis, I study the left adjoint <strong>D</strong> 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 <strong>D</strong>(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 <em>G</em>, the ∞-category of genuine <em>G</em>-spectra is obtained from the ∞-category of naive <em>G</em>-spectra by freely adjoining duals for compact objects, while respecting colimits.</p>