Exact model structures and recollements

TL;DR

This paper demonstrates how to derive recollements of triangulated categories through exact model structures, providing model categorical insights into classical and modern recollement scenarios in homotopy theory.

Contribution

It introduces a method to obtain recollements using exact model structures and connects these to classical and recent recollement examples in triangulated categories.

Findings

Model categorical explanations for Verdier localization recollement

Extension of recollement techniques to homotopy categories of chain complexes

Unification of classical and modern recollement scenarios

Abstract

We show how to obtain recollements of triangulated categories using the theory of exact model structures. After noting how the theory relates to well-known notions in the simplest case of Frobenius categories, we apply these ideas to recollements of homotopy categories of chain complexes. In short, we give model categorical explanations for the classical Verdier localization recollement as well as several recollement situations due to Neeman and Murfet.