Equivariant map

In mathematics, an equivariant map is a function between two sets that commutes with the action of a group. Specifically, let G be a group and let X and Y be two associated G-sets. A function f : X → Y is said to be equivariant if

f(g·x) = g·f(x)

for all g ∈ G and all x in X. Note that if one or both of the actions are right actions the equivariance condition must be suitably modified:

f(x·g) = f(x)·g ; (right-right)

f(x·g) = g⁻¹·f(x) ; (right-left)

f(g·x) = f(x)·g⁻¹ ; (left-right)