Homology, Homotopy and Applications
Volume 6 (2004)
Non-abelian cohomology via parity quasi-complexes
Pages: 49 – 58
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.
2010 Mathematics Subject Classification
Primary 18G10, 18G55, 57T30. Secondary 18G25.