Recollements arising from cotorsion pairs on extriangulated categories

TL;DR

This paper constructs recollements of additive categories from cotorsion pairs on extriangulated categories, generalizing previous triangulated case results and revealing new phenomena in exact categories, with applications including Krause's recollement.

Contribution

It introduces a method to derive recollements from cotorsion pairs on extriangulated categories, extending existing theories and providing new insights and applications.

Findings

Generalizes recollement construction to extriangulated categories

Reveals new phenomena in exact categories

Provides elementary proofs for Krause's recollement

Abstract

This paper is devoted to constructing some recollements of additive categories associated to concentric twin cotorsion pairs on an extriangulated category. As an application, this result generalizes the work by Chen-Liu-Yang in a triangulated case. Moreover, it highlights new phenomena when it applied to an exact category. Finally, we give some applications to illustrate our main results. In particular, we obtain the Krause's recollement whose the proofs are both elementary and very general.