# Pseudo-dualizing complexes and pseudo-derived categories

## TL;DR

This paper introduces pseudo-dualizing complexes, which relax the injective dimension condition of dualizing complexes, and shows they induce equivalences between pseudo-derived categories in ring theory.

## Contribution

It defines pseudo-dualizing complexes and demonstrates their role in establishing triangulated equivalences between pseudo-coderived and pseudo-contraderived categories for associative rings.

## Key findings

- Pseudo-dualizing complexes generalize dualizing complexes by dropping injective dimension constraints.
- They induce triangulated equivalences between pseudo-coderived and pseudo-contraderived categories.
- The construction uses generalized derived functors and module classes.

## Abstract

The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions. In the specific setting of a pair of associative rings, we show that the datum of a pseudo-dualizing complex induces a triangulated equivalence between a pseudo-coderived category and a pseudo-contraderived category. The latter terms mean triangulated categories standing "in between" the conventional derived category and the coderived or the contraderived category. The constructions of these triangulated categories use appropriate versions of the Auslander and Bass classes of modules. The constructions of derived functors providing the triangulated equivalence are based on a generalization of a technique developed in our previous paper arXiv:1503.05523.