  We prove that if G is the circle group or a profinite group, then the all of
the homotopical information of the category of rational G-spectra is captured
by triangulated structure of the rational G-equivariant stable homotopy
category. That is, for G profinite or S1, the rational G-equivariant stable
homotopy category is rigid. For the case of profinite groups this rigidity
comes from an intrinsic formality statement, so we carefully relate the notion
of intrinsic formality of a differential graded algebra to rigidity.
