Special precovering classes in comma categories

Abstract

Let T be a right exact functor from an abelian category B into another abelian category A . Then there exists a functor p from the product category A × B to the comma category (T ↓ A ). In this paper, we study the property of the extension closure of some classes of objects in (T ↓ A ), the exactness of the functor p and the detail description of orthogonal classes of a given class induced by p. Moreover, we characterize when special precovering classes in abelian categories A and B can induce special precovering classes in (T ↓ A ). As an application, we prove that under suitable cases, the class of Gorenstein projective left Λ-modules over a triangular matrix ring Λ = R M O S is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering. Consequently, we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them.