I'm interested in a text book reference on the functoriality of the Atiyah–Hirzebruch spectral sequence. The only reference I found is the script by Kupers. Help would be greatly appreciated.
2026-03-26 19:05:18.1774551918
Functoriality of Atiyah-Hirzebruch spectral sequence - Reference Request
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The AHS sequence can beconstructed by choosing a CW decomposition of the base and pulling it back to the total space. Hence, it suffices that one may choose CW decompositions to be functorial. The easisest way to do this is first to choose a functorial CW approximation such as $|\mathsf{Sing}(X)|$ and then picking the canonical CW decomposition of this geometrical realization. This is what that script is saying.