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Periodic Table standard table large table Chemical Elements ... Category theory Category:Homological algebra Homological algebra is a collection of algebraic techniques that originated in the study of algebraic topology but has also found applications to group theory and algebraic geometry Subcategories There are 3 subcategories to this category. H Homology theory K K-theory S Sheaf theory Articles in category "Homological algebra" There are 42 articles in this category. Abelian category Algebraic K-theory C Chain complex Cohomology Commutative diagram Cyclic homology D Derived category Derived functor Diagram chasing E Étale cohomology Exact functor Exact sequence Ext functor F Five lemma F cont. Flat module G Galois cohomology Gerbe Gluing axiom Grothendieck group ... Group cohomology H Hilbert's syzygy theorem Homological algebra Homological conjectures in commutative algebra I Injective module K Koszul complex L List of homological algebra topics M Mitchell's embedding theorem Motive (algebraic geometry) N Nine lemma P Projective module S Schur multiplier Severi-Brauer variety Sheaf cohomology Short five lemma ... Splitting lemma T Tor functor Triangulated category U Universal coefficient theorem W Weil conjectures Categories Algebra Abstract algebra ... Category theory The contents of this article are licensed from Wikipedia.org

62. Article About "Homological Algebra" In The English Wikipedia On 24-Apr-2004 The Homological algebra reference article from the English Wikipedia on 24Apr-2004 (provided by Fixed Reference snapshots of Wikipedia from wikipedia.org) http://fixedreference.org/en/20040424/wikipedia/Homological_algebra

The Homological algebra reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) Homological algebra Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been described for topological spaces, sheaves , and groupss ; also for Lie algebras, C-star algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. There are also other homological functors that take their place in the theory, such as Ext and Tor. There have been attempts at 'non-commutative' theories, which extend first cohomology as torsors (which is important in Galois cohomology). Foundational aspects The methods of homological algebra start with use of the exact sequence to perform actual calculations. With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts, before the subject settled down. An approximate history can be stated as follows: Cartan-Eilenberg: as in their eponymous book, used projective and injective module resolutions.

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66. Bambooweb: Homological Algebra Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. http://www.bambooweb.com/articles/h/o/Homological_algebra.html

Homological algebra Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been described for topological spaces sheaves , and groups ; also for Lie algebras C-star algebras . The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. There are also other homological functors that take their place in the theory, such as Ext and Tor . There have been attempts at 'non-commutative' theories, which extend first cohomology as torsors (important in Galois cohomology). Top Foundational aspects The methods of homological algebra start with use of the exact sequence to perform actual calculations. With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts, before the subject settled down. An approximate history can be stated as follows: Cartan-Eilenberg: as in their eponymous book, used projective and injective module resolutions 'Tohoku': the approach in a celebrated paper by Alexander Grothendieck using the abelian category concept (to include sheaves of abelian groups).

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68. Homological Algebra - Free Encyclopedia Homological algebra. From Wacklepedia The Free Encyclopedia. Homological algebra is that branch of mathematics which studies the methods of homology and http://www.wacklepedia.com/h/ho/homological_algebra.html

Wacklepedia Home Page Index Homological algebra From Wacklepedia - The Free Encyclopedia Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been described for topological spaces, sheaves , and groupss ; also for Lie algebras, C-star algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. There are also other homological functors that take their place in the theory, such as Ext and Tor. There have been attempts at 'non-commutative' theories, which extend first cohomology as torsors (which is important in Galois cohomology). Foundational aspects The methods of homological algebra start with use of the exact sequence to perform actual calculations. With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts, before the subject settled down. An approximate history can be stated as follows: Cartan-Eilenberg: as in their eponymous book, used projective and injective module resolutions.

69. Encyclopedia Database Encyclopedia Database, News continually updated from thousands of sources on the web. http://en.encyclopedia.livepress.com/index.php/Homological_algebra

_@import "http://livepress.com/ie50.css"; All Themes Business Education Entertainment ... Encyclopedia Database Encyclopedia Database Related: Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been defined for many different objects such as topological spaces sheaves groups rings ... Lie algebras , and C*-algebras . The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology Central to homological algebra is the notion of exact sequence ; these can be used to perform actual calculations. A classical tool of homological algebra is that of derived functor ; the most basic examples are Ext and Tor Foundational aspects With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts before the subject settled down. An approximate history can be stated as follows: Cartan Eilenberg : In their 1956 book "Homological Algebra", these authors used projective and injective module resolutions 'Tohoku': The approach in a celebrated paper by Alexander Grothendieck which appeared in the Second Series of The Tohoku Mathematical Journal in 1957, using the

70. MBceo.com Homological Algebra | Information About Homological Algebra Homological algebra information, websites, articles, links, and books all in one place. http://mbceo.com/more_information.php?c=Homological_algebra

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Arthritis Pain Joint Pain Chronic Pain Knee Pain ... Pain Medication Arthritis Pain Relief It's what many of us seek. What causes it and what are it's cures? You'll find your answers to Arthritis and other common forms of pain here. Categories Homological algebra Abstract algebra Algebraic topology ... Algebraic geometry Homological algebra Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been defined for many different objects such as topological spaces sheaves groups rings ... Lie algebras , and C-star algebras . The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. Central to homological algebra is the notion of exact sequence ; these can be used to perform actual calculations. A classical tool of homological algebra is that of derived functor ; the most basic examples are Ext and Tor Foundational aspects With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts before the subject settled down. An approximate history can be stated as follows:

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Homological algebra Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology Cohomology theories have been described for topological spaces, sheaves , and groupss ; also for Lie algebras, C-star algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. There are also other homological functors that take their place in the theory, such as Ext and Tor. There have been attempts at 'non-commutative' theories, which extend first cohomology as torsors (which is important in Galois cohomology). Foundational aspects The methods of homological algebra start with use of the exact sequence to perform actual calculations. With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts, before the subject settled down. An approximate history can be stated as follows: Cartan-Eilenberg: as in their eponymous book, used projective and injective module resolutions. 'Tohoku': the approach in a celebrated paper by Alexander Grothendieck using the abelian category concept (to include sheaves of abelian groups).

73. Mapping Cone (Homological Algebra) - TripAtlas.Com In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. http://tripatlas.com/Mapping_cone_(homological_algebra)

Discover Destinations Go TRAVEL GUIDE research your trip TRAVEL DIRECTORY find a travel company ... go away for less Member Login Login: Password: Join TripAtlas.com Mapping cone (homological algebra) About Mapping cone (homological algebra) In homological algebra , the 'mapping cone' is a construction on a map of chain complexes inspired by the analogous construction in topology . In the theory of triangulated categories it is a kind of combined kernel and cokernel : if the chain complexes take their terms in an abelian category , so that we can talk about cohomology , then the cone of a map ''f'' being acyclic means that the map is a quasi-isomorphism ; if we pass to the derived category of complexes, this means that ''f'' is an isomorphism there, which recalls the familiar property of maps of group s, modules over a ring , or elements of an arbitrary abelian category that if the kernel and cokernel both vanish, then the map is an isomorphism. If we are working in a t-category , then in fact the cone furnishes both the kernel and cokernel of maps between objects of its core. Contents Definition Properties Mapping cylinder Topological inspiration ... References Definition The cone may be defined in the category of chain complexes over any additive category (i.e., a category whose morphisms form abelian groups and in which we may construct a

74. Homological Algebra - Enyclopaedia Article About Homological Algebra Homological algebra encyclopaedia article Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a http://www.pro-researcher.co.uk/encyclopaedia/english/homological_algebra

Professional Researcher's Encyclopaedia Knowledge is only a click away Homological algebra - enyclopaedia article Homological algebra Summary: Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology. Cohomology theories have been described for topological spaces, sheaves, and groupss; also for Lie algebras, C-star algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology. There are also other homological functors that take their place in the theory, such as Ext and Tor. ... read the full Homological algebra article Buy Homological algebra related products: Buy from Amazon.co.uk Books Music Classical VHS ... Toys Buy from Amazon.com Books Music Classical VHS ... Toys Buy from Amazon.ca Books Music Classical VHS ... Software Buy from Amazon.de document.write('Books'); document.write('Music'); document.write('Classical'); document.write('VHS'); document.write('DVD'); document.write('Video-games');

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