A Derived Gabriel–Popescu Theorem for t-Structures via Derived Injectives

We prove a derived version of the Gabriel-Popescu theorem in framework dg-categories and t-structures. This exhibits any pretriangulated dg-category with suitable t-structure (such that its heart is Grothendieck abelian category) as t-exact localization dg-modules. give an original proof based on generalization Mitchell's argument "A quick Gabriel-Popesco theorem" involving injective objects. As application, we also short categories have unique dg-enhancement.