Actor of categories internal to groups

2018/05/28 by Şahan, Tunçar
#08A35 #18D35 #20L05 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.10951

Abstract

In this study, using the Brown-Spencer theorem and in the ligth of the works of Norrie, in the category of internal categories within groups, also called group-groupoids, we interpret the notion of actor of a crossed module over groups. Further, we construct the action of a group-groupoid on a group-groupoid. Moreover, we give the explicit construction of semi-direct product of two group-groupoids and of holomorph of group-groupoids.

Related

• Groupoids and cogroupoids: an one object approach
• Group Objects and Internal Categories
• Categorified groupoid-sets and their Burnside ring
• Action representability of the category of internal groupoids
• Actors in categories of interest