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arXiv · 0902.0161

Group cohomology with coefficients in a crossed-module

Behrang Noohi
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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.

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Behrang Noohi. 2009-02-01. Group cohomology with coefficients in a crossed-module. https://arxiv.org/abs/0902.0161

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