A homotopy theory of additive categories with suspensions

TL;DR

This paper develops a homotopy theory framework for additive categories with suspensions, extending model category concepts to exact categories and establishing equivalences with subfactor categories.

Contribution

It introduces a homotopy theory for additive categories with endofunctors and constructs the homotopy category of a Hovey triple in exact categories.

Findings

Homotopy category of an exact model structure is equivalent to a subfactor category.

Establishes a pre-triangulated structure on cofibrant-fibrant objects.

Extends homotopy theory concepts to additive and exact categories.

Abstract

We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion pairs) in an arbitrary exact category. We show that the homotopy category of an exact model structure (in the sense of Hovey) in a weakly idempotent complete exact category is equivalent to the subfactor category of cofibrant-fibrant objects as pre-triangulated categories.