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Ah, thanks.
added a section “Applications – In equivariant homotopy theory” (here) with this remark:
Compact Lie groups make a somewhat unexpected appearance as equivariance groups in equivariant homotopy theory, where the compact Lie condition on the equivariance group is needed in order for (the available proofs of) the equivariant Whitehead theorem to hold.
added brief mentioning of the equivariant triangulation theorem under “Properties” (here)
added pointer to:
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