Tannakian reconstruction in derived algebraic geometry

We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than $\mathbb{E}_\infty$-rings. In this setting, symmetric monoidal $\infty$-categories are replaced by the $\Theta$-categories of Nuiten--To\"en. These are enhancements of symmetric monoidal $\infty$-categories which capture the strict commutativity structure on animated rings.