t-structures and twisted complexes on derived injectives

In the paper Deformation theory of abelian categories, the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective objects. We show a generalization of this to pretriangulated dg-categories with a left bounded non-degenerate t-structure with enough derived injectives, the latter being derived enhancements of the injective objects in the heart of the t-structure. Such dg-categories (with an additional hypothesis of closure under suitable products) can be completely described in terms of left bounded twisted complexes of their derived injectives. (C) 2021 Elsevier Inc. All rights reserved.

Publication year:2021

Keywords:Pretriangulated dg-categories, t-structures, Derived injectives, Twisted complexes

BOF-keylabel:yes

IOF-keylabel:yes

BOF-publication weight:3

Authors:International

Authors from:Higher Education

Accessibility:Open