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Jan 28, 2016 at 17:52 comment added Bruno Stonek Dear Professor May, thank you for your reply. I now realize that this answer is addressing my confusion in the original post, wanting an equivalence between those functors Spaces --> Spaces with the category of homology theories, while what I really wanted (as Denis Nardin guessed) is the equivalence between those functors with the homotopy category of spectra. The issues of phantomness, which you had already addressed here, are not what I wanted to get at (but I didn't realize that when I wrote the question).
Jan 9, 2016 at 21:19 history answered Peter May CC BY-SA 3.0