(Co)homology of crossed modules with coefficients in a π₁-module

2003/06/04 by Simona Paoli, Paoli, Simona
Mathematics · #18G30 #18G50 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18G30 #msc:18G50

paper · pdf · doi:10.48550/arxiv.math/0306079

32 pages, LaTeX2e, Paul Taylor's diagram package; added reference. Accepted for publication by Homology, Homotopy and Applications

openalex publication_date 2003/06/04 · arxiv created 2003/07/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a cotriple (co)homology of crossed modules with coefficients in a π₁-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.

Related

• Group cohomology with coefficients in a crossed-module
• Crossed modules and cohomology of algebras over an operad
• Cyclic Homologies of Crossed Modules of Algebras
• On the nonabelian cohomology with coefficients in a crossed module
• On the non-balanced property of the category of crossed modules in groups