doiSerbia

Crossed modules, double group-groupoids and crossed squares

Temel Sedat (Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey), sedat.tel@erdogan.edu.tr
Şahan Tunşar (Department of Mathematics, Aksaray University, Aksaray, Turkey), tuncarsahan@gmail.com
Mucuk Osman (Department of Mathematics, Erciyes University, Kayseri, Turkey), mucuk@erciyes.edu.tr

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.

Keywords: Group-groupoid, crossed module, double group-groupoid, crossed square