Cohomology of categories and extensions of twisted diagrams of groups
type: Item
instance of: scholarly article
title: Cohomology of categories and extensions of twisted diagrams of groups
zbMATH Open document ID: 1247.18010
author: Olga Ziemiańska
published in: Journal of Pure and Applied Algebra
publication date: 2012-01-24T00:00:00Z
review text: If \(G\) and \(N\) are groups and let \(G\rightarrow Out(N)\) be a group homomorphism. The question if this morphism comes from an extension of \(G\) by \(N\) is decided by the vanishing of an element in \(H^3(G,Z(N))\). The equivalence classes of extensions are parameterised by \(H^2(G,Z(N))\). In the paper under review the author defines \({\mathcal R}ep\), the category whose objects are groups and morphisms from \(G\) to \(H\) are group homomorphisms from \(G\) to \(H\) modulo inner automorphisms of \(H\). The author develops an analogous theory replacing groups by functors from an indexing category \({\mathcal C}\) to \({\mathcal R}ep\).
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 18A05
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20J06
zbMATH DE Number: 5999978
zbMATH Keywords: group cohomology
zbMATH Keywords: twisted diagram of groups
MaRDI profile type: Publication
full work available at URL: j.jpaa.2011.07.008
OpenAlex ID: W2068967896
cites work: Q4319806
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DOI: 10.1016/J.JPAA.2011.07.008
description: scientific article; zbMATH DE number 5999978