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Let $Sset$ denote the category of simplicial sets with its Quillen model structure, when is a functor $F: (ho Sset)^{op} \to Ab$ representable? With $Ab$ category of Abelian groups. There is probably some classical references but my googlefu wasn't strong enough. I am hoping it would just be the direct translation of Brown representability theorem for $Ab$ valued cofunctors on $hoTop$.

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On second thought I think one can just prove that speculation directly using Quillen equivalence between the two model categories. –  yasha Apr 10 '13 at 21:58

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up vote 3 down vote accepted

There is a second classical paper by Brown himself which abstracts his original paper:

Brown, Edgar H., Jr. Abstract homotopy theory. Trans. Amer. Math. Soc. 119 1965 79–85.

I think you will find that it applies directly. Of course, that was well before model categories.

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looks good, thanks! –  yasha Apr 11 '13 at 1:36

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