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I'm interested in a text book reference on the functoriality of the Atiyah–Hirzebruch spectral sequence. The only reference I found are these lecture notes by Kupers (link should lead to the target page 52). Help would be greatly appreciated.

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A reference for the claim is Theorem 2.1 in the paper A Generalization of the Atiyah–Hirzebruch Spectral Sequence by Mehdi Hakim-Hashemi and Donald W. Kahn.

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    $\begingroup$ I expect it is in Dyer's book "Cohomology Theories": MR0268883 Dyer, Eldon . Cohomology theories. Mathematics Lecture Note Series W. A. Benjamin, Inc., New York-Amsterdam 1969 but my copy is in my office, and I don't get there very often right now. $\endgroup$
    – Robert Bruner
    Commented Aug 10, 2020 at 21:33

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