Crossed modules, double group-groupoids and crossed squares
Sedat Temel, Tunçar Şahan, Osman Mucuk
Abstract
The purpose of this paper is to obtain the notion of crossed module over group-groupoids considering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids. This equivalence enables us to produce various examples of double groupoids. We also prove that crossed modules over group-groupoids are equivalent to crossed squares.
Topics & Concepts
MathematicsEquivalence (formal languages)Categorical variableGroup (periodic table)Pure mathematicsAlgebra over a fieldStatisticsChemistryOrganic chemistryHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in AlgebraAlgebraic structures and combinatorial models