 Representability of cohomology by Eilenberg–MacLane spaces (source code)

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= Representability of cohomology by Eilenberg–MacLane spaces
{title2=$[X,K(G,n)]\cong H^n(X;G)$}

For a <CW complex> $X$, abelian $G$ and $n\geq1$, <homotopy> classes of maps to the <Eilenberg–MacLane space> correspond to <cohomology> classes by pullback of the <universal cohomology class of an Eilenberg–MacLane space>. Pointed maps give the reduced version. This converts a <cohomology> class into an actual map realizing its effect on <homotopy>.

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