2004/10/07 by V. Blanco, Víctor Blanco, Manuel Bullejos +5
Mathematics · #18D05 #18G50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:18D05 #msc:18G50
paper · pdf · doi:10.48550/arxiv.math/0410202
arxiv created 2004/10/07 · openalex publication_date 2004/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By regarding the classical non abelian cohomology of groups from a 2-dimensional categorical viewpoint, we are led to a non abelian cohomology of groupoids which continues to satisfy classification, interpretation and representation theorems generalizing the classical ones. This categorical approach is based on the fact that if groups are regarded as categories, then, on the one hand, crossed modules are 2-groupoids and, cocycles are lax 2-functors and the cocycle conditions are precisely the coherence axioms for lax 2-functors, and, on the other hand group extensions are fibrations of categories. Furthermore, n-simplices in the nerve of a 2-category are lax 2-functors.