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I'm in trouble in understanding these two statements in Morita's Geometry of Characteristic Classes book:

  1. First: enter image description here

    what's up with the "twisted" product $K(\pi_2(X),2)\times_{k^4} K(\pi_3(X),3)\cdots\times \cdots$? How is it defined?

  2. Second: enter image description here

    Is $\mathbb Q[\iota]$ the polynomial ring in the "variable"/cohomology class $\iota$? And what about $E_\mathbb Q(\iota)$: in which sense it is "the exterior algebra" over $\mathbb Q$?

I strongly suspect that the problem is "mine" in the sense that I'm not really into these topics. Any kind of reference is appreciated!

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    I think it's slightly better to think of the polynomial algebra and the exterior algebra as both being cases of a free dg commutative algebra on an even and odd degree generator, respectively. Then, the EM spaces give you the same kinds of algebras.2012-12-17

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