Let X , Y 𝑋 𝑌 X,Y be a pair of G-Sets. A map f : X → Y : 𝑓 → 𝑋 𝑌 f:X\to Y is an equivariant function if for all x : X , g : G : 𝑥 𝑋 𝑔 : 𝐺 x:X,g:G , f ( g ⋅ x ) = g ⋅ f ( x ) 𝑓 ⋅ 𝑔 𝑥 ⋅ 𝑔 𝑓 𝑥 f(g\cdot x)=g\cdot f(x) .