The homotopy category of pseudofunctors and translation cohomology
type: Item
instance of: scholarly article
title: The homotopy category of pseudofunctors and translation cohomology
zbMATH Open document ID: 1124.18004
author: Hans-Joachim Baues
author: Fernando Muro
published in: Journal of Pure and Applied Algebra
publication date: 2007-09-03T00:00:00Z
review text: Homotopy categories, track categories are categories enriched by groupoids. We are in the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations. The translation cohomology is introduced in order to classify endomorphisms in the previous 2-category. The obstruction theory here developed is defined in the Baues-Wirsching cohomology of categories. Some element of a third cohomology of \({\mathcal A}\) vanishes if and only if there exists a pseudofunctor \({\mathcal A}\to {\mathcal B}\) satisfying some property. An interpretation of this obstruction is given in terms of exact sequences for functors and linear extensions of categories.
reviewed by: Georges Hoff
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 55S35
zbMATH DE Number: 5186664
zbMATH Keywords: track category
zbMATH Keywords: obstruction
zbMATH Keywords: extension of categories
zbMATH Keywords: cohomology of categories
MaRDI profile type: Publication
full work available at URL: j.jpaa.2007.04.008
OpenAlex ID: W2081076210
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DOI: 10.1016/J.JPAA.2007.04.008
description: scientific article; zbMATH DE number 5186664