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Bar complex

In mathematics, the bar complex, also called the bar resolution, bar construction, standard resolution, or standard complex, is a way of constructing resolutions in homological algebra. It was first introduced for the special case of algebras over a commutative ring by Samuel Eilenberg and Saunders Mac Lane, and Henri Cartan and Eilenberg and has since…

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Definition

AlgebraModuleComplex
3 related topics

Resolutions

FreeBimodules
2 related topics

Overview

ResolutionsHomological algebraCommutative ringSamuel EilenbergSaunders Mac Lane
6 related topics

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Overview

Definition

Resolutions

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Bar complex

Nodes15
Edges14
Triples10
Avg. degree1.87
Density0.133333
Components1

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Bar complex

Top relations

related to Free Resolution of a Module · 5
Bar complex → Bar, Explicitly, Let, Then, This
related to Definition · 3
Bar complex → Bar, Let, Then
related to Resolutions · 2
Bar complex → However, The

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Important terminology

complex displaystyle bar resolution free resolutions one operatorname otimes algebra -module left eilenberg mac lane see also -modules -bimodules mathematics

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bar complexrelated to DefinitionLet0.60section
Bar complexrelated to DefinitionThen0.60section
Bar complexrelated to DefinitionBar0.60section
Bar complexrelated to Free Resolution of a ModuleLet0.60section
Bar complexrelated to Free Resolution of a ModuleThen0.60section
Bar complexrelated to Free Resolution of a ModuleBar0.60section
Bar complexrelated to Free Resolution of a ModuleExplicitly0.60section
Bar complexrelated to Free Resolution of a ModuleThis0.60section
Bar complexrelated to ResolutionsThe0.60section
Bar complexrelated to ResolutionsHowever0.60section

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    Min side: 3
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