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1. • CommentRowNumber1.
   • CommentAuthorAli Caglayan
   • CommentTimeOct 12th 2018
   • (edited Oct 12th 2018)
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   Author: Ali Caglayan
   Format: MarkdownItexStart of Eilenberg-MacLane space article. Naming of the constructors is not really ideal, but I don't like the ones in the original paper. The recursion principle is there it may need some more explaining. I have neglected the induction principle for now. Also I have made $G$ an arbitary group, yet the construction of higher EM-spaces require it to be abelian. Given the definition of the higher EM-spaces I don't see what is stopping it from being non-abelian. I would guess that $K(G,2)$ would have $\pi_2$ as the abelianisation of $G$. Which may be interesting. <a href="https://ncatlab.org/homotopytypetheory/revision/Eilenberg-MacLane+spaces/1">v1</a>, <a href="https://ncatlab.org/homotopytypetheory/show/Eilenberg-MacLane+spaces">current</a>

   Start of Eilenberg-MacLane space article.

   Naming of the constructors is not really ideal, but I don’t like the ones in the original paper. The recursion principle is there it may need some more explaining. I have neglected the induction principle for now.

   Also I have made $G$ an arbitary group, yet the construction of higher EM-spaces require it to be abelian. Given the definition of the higher EM-spaces I don’t see what is stopping it from being non-abelian. I would guess that $K(G,2)$ would have $\pi_2$ as the abelianisation of $G$. Which may be interesting.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 12th 2018
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   Author: Mike Shulman
   Format: MarkdownItexYes, if you write down the construction of "$K(G,n)$" for nonabelian $G$, then you should end up with $K(G_{ab},n)$ when $n\gt 1$. Given the construction $K(G,2) = \Vert \Sigma K(G,1) \Vert_2$, this should be a special case of the Hurewicz theorem.

   Yes, if you write down the construction of “$K(G,n)$” for nonabelian $G$, then you should end up with $K(G_{ab},n)$ when $n\gt 1$. Given the construction $K(G,2) = \Vert \Sigma K(G,1) \Vert_2$, this should be a special case of the Hurewicz theorem.

3. • CommentRowNumber3.
   • CommentAuthorAli Caglayan
   • CommentTimeOct 12th 2018
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   Author: Ali Caglayan
   Format: MarkdownItex@Mike Do you know if anybody has written down a proof of Hurewicz in HoTT yet? Even if it's on an evelope?

   @Mike Do you know if anybody has written down a proof of Hurewicz in HoTT yet? Even if it’s on an evelope?

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeOct 13th 2018
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   Author: Mike Shulman
   Format: MarkdownItexI don't think so.

   I don’t think so.