Group cohomology with coefficients in a crossed-module
K-Theory and Homology
2010-01-26 v3 Category Theory
Abstract
We compare three different ways of defining group cohomology with coefficients in a crossed-module: 1) explicit approach via cocycles; 2) geometric approach via gerbes; 3) group theoretic approach via butterflies. We discuss the case where the crossed-module is braided and the case where the braiding is symmetric. We prove the functoriality of the cohomologies with respect to weak morphisms of crossed-modules and also prove the "long" exact cohomology sequence associated to a short exact sequence of crossed-modules and weak morphisms.
Cite
@article{arxiv.0902.0161,
title = {Group cohomology with coefficients in a crossed-module},
author = {Behrang Noohi},
journal= {arXiv preprint arXiv:0902.0161},
year = {2010}
}
Comments
A discussion on braided 2-crossed-modules added to Section 5.3. References added