Enochs conjecture for cotorsion pairs over recollements of exact categories

Abstract

Let (A,C,ℬ)\left({\mathcal{A}},{\mathcal{C}},{\mathcal{ {\mathcal B} }}) be a recollement of exact categories. An explicit procedure about gluing complete hereditary cotorsion pairs from A{\mathcal{A}} and ℬ{\mathcal{ {\mathcal B} }} to C{\mathcal{C}} has been established by Hu et al. to provide a new method on the construction of recollements of triangulated categories. In this article, we study when the validity of Enochs conjecture for the left-hand classes of those complete hereditary cotorsion pairs is preserved in the aforementioned gluing procedure. Applications are given to cotorsion pairs induced by the class of projective objects or Gorenstein projective objects over comma categories.

Keywords

• cotorsion pair
• enochs conjecture
• recollement of exact categories
• 18g10
• 18g25
• 16d90