Higher cohomologies of modules
type: Item
instance of: scholarly article
title: Higher cohomologies of modules
zbMATH Open document ID: 1254.18006
published in: Algebraic \& Geometric Topology
publication date: 2012-05-16T00:00:00Z
review text: If \(\mathcal C\) is a small category, then a right \(\mathcal C\)-module is a contravariant functor from \(\mathcal C\) into abelian groups. The paper introduces an approach for level-\(r\) cohomology theory for \(\mathcal C\)-modules for each integer \(r\). Applications to the homotopy classification of braided and symmetric \(\mathcal C\)-fibred categorical groups and their homomorphisms are given.
reviewed by: Jiří Rosický
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 6035480
zbMATH Keywords: module
zbMATH Keywords: simplicial set
zbMATH Keywords: Eilenberg-Mac Lane complex
zbMATH Keywords: homotopy colimit
zbMATH Keywords: cohomology
zbMATH Keywords: fibred braided monoidal category
MaRDI profile type: Publication
full work available at URL: agt.2012.12.343
OpenAlex ID: W2033738660
cites work: Butterflies. I: Morphisms of 2-group stacks
cites work: Q3156490
cites work: Cohomology of small categories
cites work: Q4304740
cites work: Extensions of symmetric cat-groups
cites work: Homotopy limits, completions and localizations
cites work: Théorie de Schreier supérieure
cites work: Q4265749
cites work: Algebraic Models of 3‐Types and Automorphism Structures for Crossed Modules
cites work: Schreier theory for central extensions of categorical groups1
cites work: Nerves and classifying spaces for bicategories
cites work: Classifying spaces for braided monoidal categories and lax diagrams of bicategories
cites work: On Graded Categorical Groups and Equivariant Group Extensions
cites work: Homotopy classification of categorial torsors
cites work: Homotopy classification of braided graded categorical groups
cites work: Homotopy classification of graded Picard categories
cites work: Homotopy theory of diagrams
cites work: Modules croisés généralisés de longueur 2
cites work: On H-Spaces with Two Nontrivial Homotopy Groups
cites work: La formule de dualite globale
cites work: Homologie nicht-additiver Funktoren. Anwendungen
cites work: Equivariant Maps Which are Self Homotopy Equivalences
cites work: Q3808872
cites work: Homotopy equivalence between diagrams of spaces
cites work: Q3218816
cites work: Cohomology Theory of Abelian Groups and Homotopy Theory III
cites work: On the groups \(H(\Pi,n)\). I
cites work: On the groups \(H(\Pi,n)\). II
cites work: Q4092157
cites work: Equivariant Brauer groups
cites work: Q5580926
cites work: Q5612510
cites work: Simplicial homotopy theory
cites work: Diagrams indexed by Grothendieck constructions
cites work: A homotopy theory for stacks
cites work: Complexe cotangent et déformations. II
cites work: Braided tensor categories
cites work: Higher Topos Theory (AM-170)
cites work: Q5815624
cites work: Q5639839
cites work: Rings with several objects
cites work: The Equivariant Serre Spectral Sequence
cites work: Q4853302
cites work: Notes on 2-groupoids, 2-groups and crossed modules
cites work: Cohomology of diagrams and equivariant singular theory
cites work: Homotopical algebra
cites work: Categories tannakiennes
cites work: Q3876103
cites work: Q4893208
cites work: Q5599216
cites work: Q4192669
DOI: 10.2140/AGT.2012.12.343
author: María Calvo
author: Antonio M. Cegarra
author: Nguyen T. Quang
description: scientific article; zbMATH DE number 6035480