Remark 1.3. One can see that if BG exists, it is unique up to weak equivalence by the Yoneda lemma and the fact that every space is weakly equivalent to a CW complex. We will construct two different models of BG, the classical one from Milnor, and one from Segal. The latter will have the advantage that B(G× G′) ∼= BG× BG′ Proposition 1.4. If EG is a weakly contractible space with a free action ...