Localization, Isomorphisms and Adjoint Isomorphism in the Category Comp(A - Mod)

  •  Bassirou Dembele    
  •  Mohamed Ben Faraj Ben Maaouia    
  •  Mamadou Sanghare    


A and B are considered to be non necessarily commutative rings and X a complex of (A - B) bimodules. The aim of this
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,-).

This work is licensed under a Creative Commons Attribution 4.0 License.