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)