An Introduction to Homological Algebra
《An Introduction to Homological Algebra》 · 第 168 页 · Definition 6.2.4
For a finite group \(G\) and a \(G\)-module \(A\), the Tate cohomology groups \(\widehat H^n(G;A)\) extend ordinary cohomology in positive degrees and homology in negative degrees, with the norm-map definitions in degrees \(0\) and \(-1\).