= Postnikov tower
{c}
{title2=$\{P_nX\}$}
A <Postnikov tower> of a connected <CW complex> $X$ consists of spaces $P_nX$ with $\pi_i(P_nX)=\pi_i(X)$ for $i\le n$ and zero for $i>n$, together with compatible maps $X\to P_nX\to P_{n-1}X$. For <simply connected> $X$, each stage is a <principal Eilenberg–MacLane fibration> with fibre $K(\pi_nX,n)$, classified by a <Postnikov invariant>. The canonical map $X\to\operatorname{holim}_nP_nX$ is a weak equivalence: in each <homotopy> degree the tower is eventually constant, so the derived inverse-limit obstruction vanishes.
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