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Homological algebra

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri…

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History

Chain complexes and homology

Foundational aspects

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Functoriality

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Homological algebra

Nodes129
Edges128
Triples89
Avg. degree1.98
Density0.015504
Components1

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Homological algebra

Top relations

related to References · 46
Homological algebra → Advanced Mathematics, Alexander, Algebra, An, Berlin, Buchsbaum, Cambridge Studies, Cambridge University Press, Charles, Classics, Course, David, Encyclopaedia, Encyclopaedia Math, English, Graduate Texts, Henri Cartan, Hilton, Homology, ISBN
related to Chain complexes and homology · 13
Homological algebra → Ab, An, Barry Mitchell, Bn, Cn, Every, For, Im, Ker, R-modules, Since, The, Zn
related to Abelian categories · 8
Homological algebra → Ab, Abelian, Alexander Grothendieck, In, More, Niels Henrik Abel, The, These
related to Foundational aspects · 6
Homological algebra → Central, Cohomology, Ext, Lie, The, Tor
is a · 3
Homological algebra → branch of mathematics that studies homology in a general algebraic setting, notion of exact sequence, study of homological functors and the intricate algebraic structures that they entail
related to Functoriality · 2
Homological algebra → Since, This
related to history · 1
Homological algebra → Homological
see also · 1
Homological algebra → Abstract

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Important terminology

algebra exact homology homological groups category sequence abelian chain complexes algebraic complex functors two objects functor topological maps derived mathematics

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Homological algebrais abranch of mathematics that studies homology in a general algebraic setting0.90text
Homological algebrais astudy of homological functors and the intricate algebraic structures that they entail0.90text
Homological algebrais anotion of exact sequence0.90text
the ext functorinstance ofHistoryHomological algebra began to be studied in its most basic form in the late 19th century as a branch of topology and in the 1940s became an independent subject with the st…0.80text
the tor functorinstance ofHistoryHomological algebra began to be studied in its most basic form in the late 19th century as a branch of topology and in the 1940s became an independent subject with the st…0.80text
among othersinstance ofHistoryHomological algebra began to be studied in its most basic form in the late 19th century as a branch of topology and in the 1940s became an independent subject with the st…0.80text
topological spacesinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text
sheavesinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text
groupsinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text
ringsinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text
Lie algebrasinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text
and Cinstance ofFoundational aspectsCohomology theories have been defined for many different objects0.80text

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