If a group G acts (see action) on sets X and Y, then a map f:X → Y is equivariant if f(g·x) = g·f(x) for all g ∈ G, x ∈ X. For example, if X is the set of triangles in the plane, Y is the set of points in the plane and G is the group of isometries, then the map f taking a triangle to its centroid is equivariant. Compare invariant.