2020/05/07 by Tamar Datuashvili, Osman Mucuk, Tunçar Şahan
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Categorical variable #Combinatorics #Congruence (geometry) #Congruence relation #Equivalence (formal languages) #Equivalence relation #Geometry #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Number theory #Pure mathematics #Topological group #Topology (electrical circuits) #math.CT #msc:18D35 #msc:20L05 #msc:20L99
paper · pdf · doi:10.1007/s40062-020-00270-4
published as Journal of Homotopy and Related Structures, 15 (3-4), 625-640 (2020) · 14 pages, research paper, LaTeX2e, xypic
arxiv created 2020/05/07 · openalex created_date 2020/05/13 · openalex publication_date 2020/11/21 · arxiv updated 2020/12/11 · openalex updated_date 2026/08/05
We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to c-groups and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.