A G -invariant element of X is x ∈ X such that g ⋅ x = x for all g ∈ G. The set of all such x is denoted X and called the G -invariants of X. When X is a G -module, X is the zeroth cohomology group of G with coefficients in X, and the higher cohomology groups are the derived functors of the functor of G -invariants.