T-structures on unbounded twisted complexes

TL;DR

This paper introduces a dg-category of unbounded twisted complexes and defines natural t-structures on them, generalizing homotopy categories of injective and projective objects in abelian categories.

Contribution

It defines a dg-category of unbounded twisted complexes and establishes natural injective and projective t-structures, extending previous work on derived injectives and projectives.

Findings

Defines a dg-category of unbounded twisted complexes.

Introduces natural injective and projective t-structures on these complexes.

Generalizes homotopy categories of injectives and projectives.

Abstract

This paper is a sequel to "T-structures and twisted complexes on derived injectives" by the same author with W. Lowen and M. Van den Bergh. We define a dg-category of unbounded twisted complexes on a dg-category, which is particularly interesting in the case of dg-categories of derived injectives or derived projectives associated to a t-structure. On such unbounded twisted complexes we define a natural "injective" and dually a "projective" t-structure. This is intended as a direct generalization of the homotopy categories of injective or projective objects of an abelian category.