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  "body": "\n## Summary\n\nA Postnikov tower of a path-connected space $X$ is a sequence of spaces $X_1 \\leftarrow X_2 \\leftarrow X_3 \\leftarrow \\cdots$ with maps from $X$.\nThe stage $X_n$ has the homotopy groups of $X$ up to degree $n$ and none above degree $n$.\nEach stage maps to the previous one by a fibration with fibre an [[Eilenberg–MacLane space|AJHEYJE5XY]].\nSo the tower builds $X$ from Eilenberg–MacLane spaces, one homotopy group at a time.\nThe extra data needed to rebuild $X$ are cohomology classes called $k$-invariants.\n\n## Explanations\n\n### L1 human\n\nThink of the homotopy groups of a space as layers.\nThe $n$-th stage of the Postnikov tower keeps the first $n$ layers and throws away all the layers above.\nGoing up the tower adds one layer at a time, and in the limit one recovers the space up to weak homotopy equivalence.\nFor example, for the circle every stage is the circle itself, since the circle has only one layer.\n",
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