Relative Homological Algebra for Bivariant K-Theory

This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated categories. We briefly recall the general theory of relative homological algebra in triangulated categories and latter specialize it to the non-equivariant and the equivariant bivariant K-thoery, where the actions on C*-algebras is by a finite cyclic group. We conclude by the explicit computation of the universal abelian invariant (which is a Mackey functor) for separable C*-algebras with the action of  \(\mathbb {Z}/4\) by automorphisms.