Cotorsion pairs in comma categories

Abstract

Let A and B be abelian categories with enough projective and injective objects, and T : A-B a left exact additive functor. Then one has a comma category (B*T). It is shown that If T : A-B is X-exact, then (*X, X) is a (hereditary) cotorsion pair in A and (*Y, Y)) is a (hereditary) cotorsion pair in B if and only if ((*X, Y ), <h(X, Y)> ) is a (hereditary) cotorsion pair in (B*T) and X and Y are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories A and B can induce special preenveloping classes in (B*T).