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- W2065715660 abstract "In this paper a nonabelian version of the Dold-Kan-Puppe theorem is provided, showing how the Moore-complex functor defines a full equivalence between the category of simplicial groups and the category of what is called ‘hypercrossed complexes of groups’, i.e. chain complexes of nonabelian groups ( G n ,δ n ) with an additional structure in the form of binary operations G 1 × G 1 → G k . We associate to a pointed topological space X a hypercrossed complex ( X ); and the functor induces an equivalence between the homotopy category of connected CW-complexes and a localization of the category of hypercrossed complexes. The relationship between ( X ) and Whitehead's crossed complex II(X) is established by a canonical surjection p: (X) → II(X) , which is a quasi-isomorphism if and only if X is a J -complex. Algebraic models consisting of truncated chain-complexes with binary operations are deduced for n -types, and as an application we deduce a group-theoretic interpretation of the cohomology groups H n ( G , A )." @default.
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- W2065715660 date "1991-10-01" @default.
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- W2065715660 title "Group-theoretic algebraic models for homotopy types" @default.
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- W2065715660 doi "https://doi.org/10.1016/0022-4049(91)90133-m" @default.
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