Recollements and n-cluster tilting subcategories

Abstract

In this paper, we study the relationship among three n-cluster tilting subcategories of triangulated categories in a recollement. Let ( D ′ , D , D ″ ) be a recollement of triangulated categories. We construct an n-cluster tilting subcategory of D by gluing together n-cluster tilting subcategories of D ′ and D ″ under certain conditions. On the other hand, we prove that an n-cluster tilting subcategory of D can induce n-cluster tilting subcategories of D ′ and D ″ . Using these two results, we give a one-to-one correspondence between some n-cluster tilting subcategories of D and pairs of n-cluster tilting subcategories of D ′ and D ″ . Furthermore, we obtain a recollement of abelian categories from a recollement of triangulated categories.