Group-2-groupoids and 2G-crossed modules

Abstract

In this paper, we introduce the notion of a group-2-groupoid as a group object in the category of 2-groupoids. We also obtain a 2G-crossed module by using the structure of a group-2-groupoid. Then we prove that the category Gp2Gd of group-2-groupoids and the category 2GXMod of 2G-crossed modules are equivalent. Mathematics Subject Classification (2010). 18D05, 18D35, 20J15, 20L05