Exact dg categories II : The embedding theorem

For an exact dg category A, we introduce its bounded dg derived category Dᵇdg( A) and establish the universal exact morphism from A to Dᵇdg( A). We prove that the dg quotient of an exact dg category by a subcategory of projective-injectives carries a canonical exact structure. We show that exact dg categories reproduce under tensor products and functor dg categories. We apply our results to 0-Auslander extriangulated categories and confirm a conjecture by Fang-Gorsky-Palu-Plamondon-Pressland for the algebraic case.