Special precovering classes in comma categories

Let T be a right exact functor from an abelian category ℬ into another $${\mathscr A}$$ . Then there exists p the product A} \times {\mathscr B}$$ to comma ( $$\left( {T \downarrow A}} \right)$$ ). In this paper, we study property of extension closure some classes objects in ), exactness and detailed description orthogonal given class $${\rm{P}}\left( {{\cal X},{\cal Y}} Moreover, characterize when special precovering categories can induce As application, prove that under suitable cases, Gorenstein projective left Λ-modules over triangular matrix ring $${\rm{\Lambda }} = \left( {\matrix{ R & M \cr 0 S } is if only both R-modules S-modules are precovering. Consequently, produce large variety examples rings such modules them.