Given (T,S,R), a Torsion-Torsion Free (T.T.F) theory in an abeiian category A with sufficient projective and injective objects. it is shown that the intersection of the full subcategories T and R is the additive category of fractions with respect to the Serre subcategory S, R ⋂ T is an abelian category. An equivalence is established between the subcategories of the projective objects of R ⋂ T and the projective objects of A in T. There is also a similar equivalence for injective objects. If T has a generating set of small projective objects, it is shown that R has a cogenerating set of indecomposable injectives.