Localization, Isomorphisms and Adjoint Isomorphism in the Category Comp(A - Mod)
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,-).
1961 ◽
Vol 254
(1039)
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pp. 155-222
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2018 ◽
Vol 1
(21)
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pp. 415-438
1971 ◽
Vol 30
(3)
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pp. 459-459
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2009 ◽
Vol 08
(05)
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pp. 601-615
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