Group Extensions of the Co-type of a Crossed Module and Strict Categorical Groups

TL;DR

This paper generalizes the concept of group extensions to those of the co-type of a crossed module, using monoidal functor obstruction theory for classification.

Contribution

It introduces a new framework for studying group extensions via crossed modules and develops a cohomology-based classification method.

Findings

Cohomology classification of these extensions established

Obstruction theory applied to monoidal functors

Framework extends traditional group extension theory

Abstract

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of monoidal functors.