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Chain complex

In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is contained in the kernel of the next. Associated to a chain complex is its homology, which is (loosely speaking) a measure of the failure…

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Category of chain complexes

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Chain complex

Nodes69
Edges68
Triples34
Avg. degree1.97
Density0.028986
Components1

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Chain complex

Top relations

related to Chain homotopy · 6
Chain complex → An, Bn, Given, It, One, The
related to de Rham cohomology · 5
Chain complex → Locally, Re, Rham, The, This
related to Exact sequences · 5
Chain complex → Ak, An, For, In, This
see also · 5
Chain complex → Buchsbaum, Differential, Eisenbud, Kan, Lie
related to Singular homology · 4
Chain complex → Define Cn, It, Let, That
related to Category of chain complexes · 3
Chain complex → Ch, Chain, If
related to Definitions · 3
Chain complex → Explicitly, It, The
is a · 2
Chain complex → algebraic structure that consists of a sequence of abelian groups, short exact sequence
related to Chain maps · 1
Chain complex → This

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Important terminology

chain complex homology displaystyle maps complexes singular map exact homomorphisms degree sequence groups abelian cochain called homotopy differential topological algebraic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Chain complexis aalgebraic structure that consists of a sequence of abelian groups0.90text
Chain complexis ashort exact sequence0.90text
Chain complexrelated to Category of chain complexesChain0.60section
Chain complexrelated to Category of chain complexesCh0.60section
Chain complexrelated to Category of chain complexesIf0.60section
Chain complexrelated to Chain homotopyGiven0.60section
Chain complexrelated to Chain homotopyAn0.60section
Chain complexrelated to Chain homotopyBn0.60section
Chain complexrelated to Chain homotopyThe0.60section
Chain complexrelated to Chain homotopyIt0.60section
Chain complexrelated to Chain homotopyOne0.60section
Chain complexrelated to Chain mapsThis0.60section

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