About: Horseshoe lemma

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In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects and to resolutions ofextensions of by . It says that if an object is an extension of by , then a resolution of can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of and . The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis.

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rdf:type	yago:WikicatLemmas yago:Abstraction100002137 yago:Communication100033020 yago:Lemma106751833 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453
rdfs:label	Hufeisenlemma (de) Horseshoe lemma (en) Horseshoe lemma (ja) Lema da ferradura (pt)
rdfs:comment	Das Hufeisenlemma gehört zu den Grundlagen der homologischen Algebra. Es besagt, dass die drei Moduln in einer kurzen exakten Sequenz so aufgelöst werden können (projektiv oder injektiv), dass eine kurze exakte Folge von Auflösungen entsteht. Das Ergebnis kommt – allerdings ohne Namen – bereits 1956 im Buch von Cartan und Eilenberg vor. (de) In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects and to resolutions ofextensions of by . It says that if an object is an extension of by , then a resolution of can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of and . The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis. (en) ホモロジー代数において、horseshoe lemma は、simultaneous resolution theorem と呼ばれることもあるが、2つの対象との分解をのによる拡張の分解に関係づけるステートメントである。それは次のようなものである。対象がのによる拡張であれば、の分解は、分解の n 番目の項がとの分解における n 番目の項の余積に等しいように帰納的に構成することができる。補題の名前は補題の仮定を描く図式の形に由来する。 (ja)
foaf:depiction
dct:subject	Homological algebra Lemmas in category theory
Wikipage page ID	4603066 (xsd:integer)
Wikipage revision ID	1112007120 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective resolution Mathematical induction Coproduct Opposite category Snake lemma Commutative diagram Nine lemma Projective object Homological algebra Abelian category Homological algebra Injective object Lemmas in category theory Exact sequence
sameAs	Horseshoe lemma Horseshoe lemma Horseshoe lemma Horseshoe lemma Horseshoe lemma Horseshoe lemma Horseshoe lemma Horseshoe lemma
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Short_description dbt:GBurl dbt:PlanetMath_attribution
thumbnail	wiki-commons:Special:FilePath/Horseshoe_lemma.png?width=300
id	7799 (xsd:integer)
title	horseshoe lemma (en)
has abstract	Das Hufeisenlemma gehört zu den Grundlagen der homologischen Algebra. Es besagt, dass die drei Moduln in einer kurzen exakten Sequenz so aufgelöst werden können (projektiv oder injektiv), dass eine kurze exakte Folge von Auflösungen entsteht. Das Ergebnis kommt – allerdings ohne Namen – bereits 1956 im Buch von Cartan und Eilenberg vor. (de) In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects and to resolutions ofextensions of by . It says that if an object is an extension of by , then a resolution of can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of and . The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis. (en) ホモロジー代数において、horseshoe lemma は、simultaneous resolution theorem と呼ばれることもあるが、2つの対象との分解をのによる拡張の分解に関係づけるステートメントである。それは次のようなものである。対象がのによる拡張であれば、の分解は、分解の n 番目の項がとの分解における n 番目の項の余積に等しいように帰納的に構成することができる。補題の名前は補題の仮定を描く図式の形に由来する。 (ja)
prov:wasDerivedFrom	wikipedia-en:Horseshoe_lemma?oldid=1112007120&ns=0
page length (characters) of wiki page	2474 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Horseshoe_lemma
is Link from a Wikipage to another Wikipage of	List of lemmas Horseshoe Lemma Grothendieck spectral sequence Cartan–Eilenberg resolution
is Wikipage redirect of	Horseshoe Lemma
is foaf:primaryTopic of	wikipedia-en:Horseshoe_lemma

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