Question: Let G be a group acting on the sets x , Y . A map f : x Y is called G - equivariant if

Let G be a group acting on the sets x,Y. A map f:xY is called G-
equivariant if f(g*x)=g*f(x) for all ginG,xinx.
(a) Show that the composition of G-equivariant maps is again G-equivariant.
(b) Show that if a G-equivariant map f is a bijection, then the inverse f-1 is
also G-equivariant. In this case we call the actions on x and Y equivalent.
Let G be a group acting on the sets x , Y . A map

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