The stabilized bounded N-derived category of an exact category

TL;DR

This paper extends Buchweitz's equivalence between singularity and stable categories to a broader setting using N-complexes within exact categories, providing foundational results for their derived categories.

Contribution

It introduces a relative categorical framework based on N-complexes, generalizing classical results and establishing foundational properties for derived categories of N-complexes.

Findings

Establishes a triangle equivalence in the N-complex setting

Provides foundational results on derived categories of N-complexes

Generalizes classical Cohen-Macaulay module results

Abstract

Buchweitz related the singularity category of a (strongly) Gorenstein ring and the stable category of maximal Cohen-Macaulay modules by a triangle equivalence. We phrase his result in a relative categorical setting based on N-complexes instead of classical 2-complexes. The role of Cohen-Macaulay modules is played by chains of monics in a Frobenius subcategory of an exact category. As a byproduct, we provide foundational results on derived categories of N-complexes over exact categories known from the Abelian case or for 2-complexes.