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The nonabelian bar resolution

Lucian M. Ionescu
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Abstract

The theory of parity quasi-complexes (PQC) is developed, preparing a set up for defining derived functors using resolutions in the nonabelian case. A homotopy structure on the category of PQC is defined, yielding a 2-category structure. The nonabelian homology functor factors through the corresponding homotopy category. Following the relative homological algebra approach, resolutions are defined as PQC having parity contracting homotopies in a suitable category. A canonical non-abelian PQC resolution for groups is defined.

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Lucian M. Ionescu. 2001-08-21. The nonabelian bar resolution. https://arxiv.org/abs/math/0108147

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