On derived categories and derived functors

TL;DR

This paper introduces a method to construct categories equivalent to derived categories of abelian categories using homological resolutions with projective or injective multicomplexes.

Contribution

It provides a new approach to model derived categories via specific multicomplexes, enhancing understanding of their structure and construction.

Findings

Constructs categories equivalent to derived categories using homological resolutions.

Defines the use of projective and injective multicomplexes for category equivalence.

Offers a framework for understanding derived categories through explicit resolutions.

Abstract

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.