Abstract

Introduction \Gamma-spaces were introduced by Segal [S], who proved that they are combinatorial models for connective spectra (see also [A], [BF]). Based on Kan-Thurston theorem we show that any \Gamma-space is stably weak equivalent to a discrete \Gamma-group. By a well-known theorem of Dold-Kan the Moore normalization establishes the equivalence between the category of simplicial abelian groups and the category of chain complexes (see [DP]). mimicking the construction of normalization of simplicial groups, we give a similar construction for \Gamma-groups. This construction is based on the notion of cross-effects of functors [BP], which is a generalizatin of the classical definition of Eilenberg and Mac Lane [EM] to the non-abelian setup. Finally a Dold-Kan type theorem for the category of \Gamma-groups is proved. In abelian case our theorem claims that the category of abelian \Gamma-groups is equivalent to the category of functors Ab\Omega , where\Om

Citations