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P~ ~ p 1 ~ P~ I ------+ M' - - O. ) I/Ji ~ H omA' (Pil ' N') ~ "', in which the maps t/J; occur. By definition, Ext~, (M', N') = ker t/J;+l/im t/J;. 42) are isomorphisms, we conclude at once that [ ® R Ext~ (M, N) ~ Ext~, (M ' , N '), n ~ 1. This is a two-sided [-isomorphism, since all of the maps occurring in the proof are two-sided [-maps. The result also holds when n = 0, if we set Ext O = Hom. This completes the proof.