Actor of categories internal to groups
Tun\c{c}ar \c{S}ahan

TL;DR
This paper explores the concept of actors within internal categories called group-groupoids, utilizing the Brown-Spencer theorem and Norrie's work to interpret actions, semi-direct products, and holomorphs of these structures.
Contribution
It provides a new interpretation of actors in group-groupoids and explicitly constructs their actions, semi-direct products, and holomorphs, extending existing theoretical frameworks.
Findings
Interpretation of actors in group-groupoids using Brown-Spencer theorem
Explicit construction of semi-direct products of group-groupoids
Development of holomorphs for group-groupoids
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Intracranial Aneurysms: Treatment and Complications
