Eilenberg–MacLane space

Summary

An Eilenberg–MacLane space $K(G, n)$ is a path-connected space whose only nonzero homotopy group is $G$ in degree $n$. Such spaces exist for every group $G$ when $n = 1$ and every abelian group $G$ when $n \ge 2$, and they are unique up to weak homotopy equivalence. They are the building blocks of all spaces in the sense of Postnikov towers. They represent ordinary cohomology: for an abelian group $G$ and a CW complex $X$, $H^n(X; G)$ is the set of homotopy classes of maps $X \to K(G, n)$.