Constructing cotorsion pairs over generalized path algebras

We introduce two adjoint pairs (e _i ^λ , ( ) _i ) and (( ) _i , e _i ^ρ ) and give a new method to construct cotorsion pairs. As applications, we characterize all projective and injective representations of a generalized path algebra and exhibit projective and injective objects of the category M _p which is a generalization of monomorphisms category.