Nonabelian $H^2$ with coefficients in a group and with coefficients in a crossed module

TL;DR

This paper extends the nonabelian second cohomology sequence to include coefficients in crossed modules, building on prior work on nonabelian first cohomology.

Contribution

It introduces an extension of the cohomology exact sequence for nonabelian H^1 to H^2 with coefficients in crossed modules, advancing the theoretical framework.

Findings

Extended the cohomology exact sequence to nonabelian H^2 with crossed module coefficients

Built upon Dedecker and Debremaeker's work on nonabelian H^1

Provided a theoretical foundation for further research in nonabelian cohomology

Abstract

In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.