Braided equivariant crossed modules and cohomology of $\Gamma $-modules

TL;DR

This paper explores the classification of braided rossed modules via braided strict ategories and generalizes Schreier theory to xtensions of ategories, advancing the understanding of ohomology of ategories.

Contribution

It introduces a classification framework for braided rossed modules and extends Schreier theory to xtensions of ategories, broadening cohomological methods.

Findings

Classification of braided rossed modules by braided strict ategories

Generalization of Schreier theory to xtensions of ategories

New insights into ohomology of ategories

Abstract

If $\Gamma $ is a group, then braided $\Gamma $-crossed modules are classified by braided strict $\Gamma $-graded categorial groups. The Schreier theory obtained for $\Gamma $-module extensions of the type of an abelian $\Gamma $-crossed module is a generalization of the theory of $\Gamma $-module extensions.