We consider two pairs of complete hereditary cotorsion theories (P, M), (M, I), and (C, L), (L, E) on the category of left R-modules, such that P subset of C. We prove that for any left R-modules M, N and for any n >= 1, the generalized Tate cohomology modules (Ext) over cap (n)(C),(P)(M, N) can be computed either using a left C-resolution ofM and a left P-resolution of M or using a right epsilon-and a right I-resolution of N.
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