Strict Gr-categories and applications on classification of extensions of groups of the type of a crossed module

TL;DR

This paper explores how Gr-category theory can be applied to classify crossed modules and group extensions of a specific type, providing new insights into their structural relationships.

Contribution

It introduces applications of Gr-category theory to classify crossed modules and related group extensions, advancing the theoretical framework in this area.

Findings

Classification of crossed modules achieved

Extensions of groups of the specified type characterized

New connections between Gr-categories and group theory established

Abstract

In this paper we state some applications of Gr-category theory on the classification of crossed modules and on the classification of extensions of groups of the type of a crossed module.