Applications of exact structures in abelian categories

In an abelian category A with small Ext groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunctors F of Ext(A)(1) (-,-) such that A has enough F-projectives and enough F-injectives and Quillen exact structures epsilon with enough epsilon-projectives and enough epsilon-injectives. In this case, we get a strengthened version of the translation of the Wakamatsu lemma to the exact context, and also prove that subcategories which are epsilon-resolving and epimorphic precovering with kernels in their right epsilon-orthogonal class and subcategories which are epsilon-coresolving and monomorphic preenveloping with cokernels in their left epsilon-orthogonal class are determined by each other. Then we apply these results to construct some (pre)enveloping and (pre)covering classes and complete hereditary epsilon-cotorsion pairs in the module category.