paper is to show that:

The functors \overline{EXT}^n_{Comp(A-Mod)}(X,-): Comp(A-Mod) \longrightarrow Comp(B-Mod) and Tor_n^{Comp(B-Mod)}(X,-): Comp(B-Mod) \longrightarrow Comp(A-Mod) are adjoint functors.

The functor S_C^{-1}() commute with the functors X\bigotimes - , Hom^{\bullet}(X,-) and their corresponding derived functors \overline{EXT}^n_{Comp(A-Mod)}(X,-) and Tor_n^{Comp(B-Mod)}(X,-).