2001/08/21 by Lucian M. Ionescu, Ionescu, Lucian M.
Mathematics · #18G25 (Secondary) #18G55 (Primary) 18G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.CT #math.GR #msc:18G10 #msc:18G25 #msc:18G55
paper · pdf · doi:10.48550/arxiv.math/0108147
AMS-LaTex, 9 pages
arxiv created 2001/08/21 · openalex publication_date 2001/08/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.