Then ( C n ( G , E ) , d n ) becomes a cochain complex and its cohomology, denoted by H d n ( G , E ) , is called the differentiable cohomology of G ⇉ ⇉ M with coefficients in E → → M . Note that, since the differential at degree zero is d 0 ( c ) ( g ) = g ⋅ ⋅ c ( s ( g ) ) − − c ( t ( g ) ) , one has always H d 0 ( G , E ) = ker ⁡ ⁡ ( d 0 ) = Γ Γ ( E ) G .