2016/01/26 by Tunçar Şahan, Şahan, Tunçar, Osman Mucuk +1
Mathematics · #20L05 #22A22 #22AXX #57M10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AT #math.CT #msc:20L05 #msc:22A22 #msc:22AXX #msc:57M10
paper · pdf · doi:10.48550/arxiv.1601.07095
30 pages, research paper, LaTeX2e, xypic
arxiv created 2016/01/26 · openalex publication_date 2016/01/26 · arxiv updated 2016/01/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups with operations and internal groupoids we prove how normality and quotient concepts are related in these two categories. Further we prove an equivalence of crossed modules over groups with operations and cat1-groups with operations for a certain algebraic category; and then by this equivalence we determine normal and quotient objects in the category of cat1-groups with operations. Finally we characterize the coverings of cat1-groups with operations.