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 $hoTop$.

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. 

