Crossed modules, double group-groupoids and crossed squares
Copyright policy )Crossed modules, double group-groupoids and crossed squares
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.
- Erciyes University Turkey
- Recep Tayyip Erdoğan University Turkey
- Aksaray University Turkey
Crossed Square, 20L05, 22A22, 18D35, 2-groups, crossed modules, crossed complexes, Categorical structures, group-groupoid, Mathematics - Category Theory, groupoid, Group-Groupoid, Groupoids (i.e. small categories in which all morphisms are isomorphisms), crossed module, Crossed Module, Double Group-Groupoid, FOS: Mathematics, Algebraic Topology (math.AT), Category Theory (math.CT), Internal categories and groupoids, double group-groupoid, Mathematics - Algebraic Topology, crossed square, Topological groupoids (including differentiable and Lie groupoids)
Crossed Square, 20L05, 22A22, 18D35, 2-groups, crossed modules, crossed complexes, Categorical structures, group-groupoid, Mathematics - Category Theory, groupoid, Group-Groupoid, Groupoids (i.e. small categories in which all morphisms are isomorphisms), crossed module, Crossed Module, Double Group-Groupoid, FOS: Mathematics, Algebraic Topology (math.AT), Category Theory (math.CT), Internal categories and groupoids, double group-groupoid, Mathematics - Algebraic Topology, crossed square, Topological groupoids (including differentiable and Lie groupoids)
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