# T-structures and twisted complexes on derived injectives

## TL;DR

This paper generalizes a reconstruction theorem for abelian categories to pretriangulated dg-categories with t-structures, showing they can be described via twisted complexes of derived injectives.

## Contribution

It extends the reconstruction of abelian categories to a broader class of dg-categories with t-structures, introducing a description through twisted complexes of derived injectives.

## Key findings

- Pretriangulated dg-categories with certain t-structures can be reconstructed from derived injectives.
- Such dg-categories are equivalent to categories of twisted complexes of derived injectives.
- The results generalize known theorems from abelian categories to dg-categories.

## Abstract

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.