 Principal Eilenberg–MacLane fibration

For an abelian group $A$, a principal fibration with fibre $K(A,n)$ is a homotopy pullback of the path fibration $PK(A,n+1)\to K(A,n+1)$. It is therefore the homotopy fibre of a map $k:B\to K(A,n+1)$ and is classified by $[k]\in H^{n+1}(B;A)$. The fibre acts by translation up to homotopy; in this untwisted description the fundamental group acts trivially on $A$. This is the principal-fibration form used for simply connected Postnikov towers.