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Non-abelian cohomology via parity quasi-complexes

Lucian M. Ionescu

The homotopy category of parity quasi-complexes is introduced. The homotopy structure is compatible with the non-abelian homology of parity quasi-complexes.

Parity contracting homotopies are defined, determining the parity free resolutions in a canonical way, enabling the nonabelian bar construction.

In this way, the even/odd grouping of the simplicial maps in the cocycle conditions of nonabelian cohomology is explained.

Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 49-58

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