On the nonabelian cohomology with coefficients in a crossed module

2020/10/12 by Pirashvili, Mariam
#Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2010.06493

Abstract

This paper is concerned with the nonabelian cohomology of groups with coefficients in crossed modules. These objects were introduced by Dedecker and studied by Breen, Borovoi, Noohi and many others. In this paper we study several important objects that are classified by these cohomologies and for them we develop a theory similar to the Schreier obstruction theory of group extensions.

Related

• Group cohomology with coefficients in a crossed-module
• Quasi-abelian crossed modules and nonabelian cohomology
• Extending the exact sequence of nonabelian H¹, using nonabelian H² with coefficients in crossed modules
• Crossed modules and symmetric cohomology of groups
• Equivariant Crossed Modules and Cohomology of Groups with Operators