Balanced systems for Hom

We present the concept of balanced systems as a tool to induce balanced pairs for Hom bifunctors with domain determined by classes of objects with finite left and right resolution dimension relative to these pairs. This approach to balance of Hom will cover several well-known ambients where its right derived functors are obtained relative to certain classes of objects in abelian categories, such as Gorenstein projective and injective modules and chain complexes, Gorenstein modules relative to Auslander and Bass classes, among others.