In the development of homological algebra, one has to prove at some point that, in defining the derived functors of ⊗ and of Hom, it makes no difference whether we resolve both variables or only one of them. Taking ⊗ ( = ⊗R) as a typical example, what has to be proved is
(A) If the complex F is projective, or even flat, as a right R-module, and if f: P → A is a projective resolution of the left R-module A, then
is an isomorphism.
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