Gluing n-tilting and n-cotilting subcategories

Abstract

Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement (A, B, C) of extriangulated categories, we show that n-tilting (resp. n-cotilting) subcategories in A and C can be glued to get n-tilting (resp. n-cotilting) subcategories in B under certain conditions.

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.…”