Torsion pairs and recollements of extriangulated categories

Abstract

In this article, we prove that if (A, B, C) is a recollement of extriangulated categories, then n-cotorsion pairs in A and C can induce n-cotorsion pairs in B. Conversely, this holds true under natural assumptions. Besides, we give mild conditions on a pseudo cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding additive quotients to form a recollement of semi-abelian categories.

Resolving subcategories and dimensions in recollements of extriangulated categories

“…Recently, gluing techniques with respect to a recollement of extriangulated categories have been investigated; for instance, He, Hu and Zhou [10] glued torsion pairs in a recollement of extriangulated categories; Liu and Zhou [18] glued cotorsion pairs in a recollement of extriangulated categories; etc. Some of results give a simultaneous generalization of recollements of abelian categories and triangulated categories.…”