Higher Algebra in t-Structured Tensor Triangulated ∞-Categories

We observe that many concepts from Lurie's Higher Algebra can be generalized to the setting of t-structured tt-∞-categories, including notions such as flatness, and étale morphisms. Under suitable conditions on a tt-∞-category, we can establish Lazard's theorem, étale rigidity, and the universal property of the derived category, among others.