Constructing cotorsion pairs over generalized path algebras

Abstract

We introduce two adjoint pairs ({{\displaystyle e}}_{\lambda }^i,{{\displaystyle ( )}}_i) and({{\displaystyle ( )}}_i,{{\displaystyle e}}_{\rho }^i) 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{{\displaystyle \mathfrak{M}}}_p which is a generalization of monomorphisms category.

Key words： Cotorsion pair; representation; generalized path algebra

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