Equivariant Crossed Modules and Cohomology of Groups with Operators

TL;DR

This paper explores equivariant crossed modules and their connection to graded categorical groups, extending classical theories of group extensions to include equivariant structures and providing a generalized Schreier theory.

Contribution

It introduces a generalized Schreier theory for equivariant group extensions based on equivariant crossed modules, linking them with strict graded categorical groups.

Findings

Established a correspondence between equivariant crossed modules and strict graded categorical groups.

Generalized classical Schreier theory to include equivariant group extensions.

Unified theories of group extensions and equivariant structures.

Abstract

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.