1:23 PM
What represents equivariant cohomology? That is, given a $G$-space $X$, is there a $G$-space $Z$ such that $H^n_G(X; \Bbb Z) := H^n(X\times_G EG; \Bbb Z) = [X, Z]_G$ naturally? Looking around tells me about "equivariant Eilenberg MacLane spaces" but these seem to represent Bredon cohomology, not Borel equivariant cohomology.

2:06 PM
@BalarkaSen I think Map(EG,K(Z,n)), viewed as a G-space by the action of G on EG, does this.

You're right, I just realized.