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1. • CommentRowNumber1.
   • CommentAuthorJon Beardsley
   • CommentTimeAug 14th 2013
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   Author: Jon Beardsley
   Format: MarkdownItexHi again! Do you guys know if anyone has developed a theory/notion of Whitehead's universal quadratic functor (often denoted $Gamma$) for simplicial group(oid)s, or just generally for presheaves valued in simplicial groups? There's an old result proving something along the lines of $H^3(BB\Pi, G)=Hom(\Gamma(\Pi),G)$, where $\Gamma$ is basically "quadratic" functions on $\Pi$, and I've been wondering if there's a better way to think about this, or a more general way. Thanks for any info! -Jon

   Hi again!

   Do you guys know if anyone has developed a theory/notion of Whitehead’s universal quadratic functor (often denoted $Gamma$) for simplicial group(oid)s, or just generally for presheaves valued in simplicial groups? There’s an old result proving something along the lines of $H^3(BB\Pi, G)=Hom(\Gamma(\Pi),G)$, where $\Gamma$ is basically “quadratic” functions on $\Pi$, and I’ve been wondering if there’s a better way to think about this, or a more general way.

   Thanks for any info! -Jon

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeAug 14th 2013
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   Author: Tim_Porter
   Format: MarkdownItexTry looking at the work by Baues (lots of reference possible) and also R. Brown and J.-L. Loday, Homotopical excision, and Hurewicz the- orems for n-cubes of spaces , Proc. London Math. Soc., (3)54, (1987), 176 – 192. It is not clear to me what you are wanting, but look at those sources first.... and write something up on them for the nLab. :-)

   Try looking at the work by Baues (lots of reference possible) and also R. Brown and J.-L. Loday, Homotopical excision, and Hurewicz the- orems for n-cubes of spaces , Proc. London Math. Soc., (3)54, (1987), 176 – 192.

   It is not clear to me what you are wanting, but look at those sources first…. and write something up on them for the nLab. :-)