Exact dg categories II : The embedding theorem

Abstract

For an exact dg category $\mathcal{A}$, we introduce its bounded dg derived category ${\mathcal{D}}_{dg}^b(\mathcal{A})$ and establish the universal exact morphism from $\mathcal{A}$ to ${\mathcal{D}}_{dg}^b(\mathcal{A})$. 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.

This paper is a revised and augmented version of the second part of the author's Ph.D thesis arXiv:2306.08231; 45 pages; comments are very welcome