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  "body": "\n## Summary\n\nAn Eilenberg–MacLane space $K(G, n)$ is a path-connected space whose only nonzero [[homotopy group|P976WYEFMB]] is $G$ in degree $n$.\nSuch 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.\nThey are the building blocks of all spaces in the sense of Postnikov towers.\nThey 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 $X \\to K(G, n)$.\n\n## Explanations\n\n### L1 human\n\nHomotopy groups measure holes of each dimension in a space.\nAn Eilenberg–MacLane space has holes of exactly one dimension, described by the group $G$.\nThe circle is $K(\\Z, 1)$: it has a one-dimensional hole, and its higher homotopy groups vanish because its universal cover, the line, is contractible.\nInfinite-dimensional complex projective space is $K(\\Z, 2)$, and infinite-dimensional real projective space is $K(\\Z/2, 1)$.\n",
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