1. Homological Algebra - Wikipedia, The Free Encyclopedia Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins http://en.wikipedia.org/wiki/Homological_algebra

Homological algebra From Wikipedia, the free encyclopedia Jump to: navigation search Homological algebra is the branch of mathematics which 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 Poincaré and David Hilbert The development of homological algebra was closely intertwined with the emergence of category theory . By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. The hidden fabric of mathematics is woven of chain complexes , which manifest themselves through their homology and cohomology . Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings , modules, topological spaces , and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences From its very origins, homological algebra has played an enormous role in algebraic topology. Its sphere of influence has gradually expanded and presently includes

2. Homological Algebra Puzzle | The N-Category Café Whenever I have time to talk with James Dolan, he likes to pose puzzles — partially to test out ideas he just had, partially to teach me stuff, and partially just to watch me http://golem.ph.utexas.edu/category/2010/07/homological_algebra_puzzle.html

@import url("/category/styles-site.css"); A group blog on math, physics and philosophy Skip to the Main Content Enough, already! Skip to the content. Note: These pages make extensive use of the latest XHTML and CSS Standards only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser. Main Day on Higher Category Theory July 1, 2010 Homological Algebra Puzzle Posted by John Baez his solution of the puzzle, but the next best thing is to solve it. Puzzle: What is the free finitely cocomplete linear category on an epi? First, remember what Tom said shibboleth , a mark of identity, or at the very least, something that any professional can do. The point I want to make is that for category theory, the ability to throw around phrases of the form the free such-and-such category containing a such-and-such Of course, it also helps to know what the words mean here:

3. Homological Algebra - Blackwell Bookshop Online Homological Algebra, Henri Cartan, S. Eilenberg, Mathematics Books Blackwell Online Bookshop http://bookshop.blackwell.co.uk/jsp/id/Homological_Algebra/9780691049915

4. Homological Algebra: Facts, Discussion Forum, And Encyclopedia Article Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from http://www.absoluteastronomy.com/topics/Homological_algebra

Home Discussion Topics Dictionary ... Login Homological algebra Homological algebra Topic Home Discussion Discussion Ask a question about ' Homological algebra Start a new discussion about ' Homological algebra Answer questions from other users Full Discussion Forum Encyclopedia Homological algebra is the branch of mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... which studies homology Homology (mathematics) In mathematics , homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group... in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology Combinatorial topology In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces were regarded as derived from combinatorial decompositions such as simplicial complexes... (a precursor to algebraic topology Algebraic topology Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism...

5. Homological Algebra - VisWiki Homological algebra Ring (mathematics), Singular homology, Alexander Grothendieck, Functor, Module (mathematics) - VisWiki http://www.viswiki.com/en/Homological_algebra

6. Homological Algebra | Ask.com Encyclopedia Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to http://www.ask.com/wiki/Homological_algebra?qsrc=3044

7. Mapping Cone (homological Algebra) - Wikipedia, The Free Encyclopedia 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 http://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)

Mapping cone (homological algebra) From Wikipedia, the free encyclopedia Jump to: navigation search 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 groups 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 ... edit 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

8. Homological Algebra - Math2033 Homological Algebra . Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins http://math2033.uark.edu/wiki/index.php/Homological_algebra

Math 2033 Forum My Links Log in Get Started How to get to work! The Basics The Sandbox Things we need for the course ... Some tasks on the wiki Navigation The Math Factor Podcast Back to the Main Page Contact Your Professors Random page Search Toolbox What links here Related changes Special pages Printable version ... Permanent link CATEGORY CLOUD Algebra Applied Areas of Math Art ... Wiki for Dummies Views Page Talk View source History Homological algebra From Math2033 Jump to: navigation search Homological Algebra Homological algebra is the branch of mathematics which 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 Poincaré and David Hilbert. The development of homological algebra was closely intertwined with the emergence of category theory. By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. The hidden fabric of mathematics is woven of chain complexes, which manifest themselves through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings, modules, topological spaces, and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences.

9. Homological Algebra Enlightenment a festival and resource dedicated to the attainment of enlightenment and the awakening of the higher self thru spiritual wisdom teachings and practises with the http://www.experiencefestival.com/homological_algebra

10. Homological Algebra 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 http://www.fact-index.com/h/ho/homological_algebra.html

Main Page See live article Alphabetical index 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.

11. Homological Algebra Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to http://www.kosmix.com/topic/Homological_algebra

12. Homological Algebra - ENotes.com Reference Get Expert Help. Do you have a question about the subject matter of this article? Hundreds of eNotes editors are standing by to help. http://www.enotes.com/topic/Homological_algebra

13. Homological Algebra - On Opentopia, Find Out More About 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. http://encycl.opentopia.com/term/Homological_algebra

About Opentopia Opentopia Directory Encyclopedia ... Tools Homological algebra Encyclopedia H HO HOM : 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 space s, sheaves group s, ring s, Lie algebra s, and C*-algebra s. 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

14. Category:Homological Algebra - Wikimedia Commons Media in category Homological algebra The following 24 files are in this category, out of 24 total. http://commons.wikimedia.org/wiki/Category:Homological_algebra

Category:Homological algebra From Wikimedia Commons, the free media repository Jump to: navigation search Subcategories This category has only the following subcategory. C Complexes (algebra) (22 F) Media in category "Homological algebra" The following 24 files are in this category, out of 24 total. AdjointFunctorsHomSe... 8,964 bytes Axiom TR3.svg 29,067 bytes Axiom TR4 (BBD).svg 53,688 bytes Axiom TR4 (caps).svg 69,550 bytes Axiom TR4 (polyhedro... 54,733 bytes Chain co morph.PNG 14,424 bytes Chain homotopy.svg 49,708 bytes Complex les.png 20,105 bytes Complex ses diagram.png 18,875 bytes DormanLuke.png 14,038 bytes Elliott's theorem 2.png 10,602 bytes Exact couple.png 1,066 bytes Homologie.jpg 50,358 bytes Mapping cone.PNG 4,557 bytes Mayer-Vietoris natur... 31,262 bytes Monomorphism-01.png 1,203 bytes NatTrafo.PNG 8,978 bytes Octahedral diagram v... 23,167 bytes Refl1.png 810 bytes Simplicial complex e... 25,118 bytes Simplicial complex e... 12,012 bytes Simplicial complex n... 25,382 bytes Spectral sequence.png 154,400 bytes Transitive-closure.svg

15. Homological Algebra - Definition 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. http://www.wordiq.com/definition/Homological_algebra

Homological algebra - Definition 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: 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 The Tohoku Mathematical Journal in 1957, using the

16. Homological Algebra - Wikivisual 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. http://en.wikivisual.com/index.php/Homological_algebra

Francais English Homological algebra From Wikipedia, the free encyclopedia Jump to: navigation search 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 edit 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

17. CiteULike: Tag Homological_algebra [12 Articles] Abstract We describe the projectives in the category of functors from a graded poset to abelian groups. Based on this description we define a related condition, pseudo http://www.citeulike.org/tag/homological_algebra

18. Homological Algebra - Discussion And Encyclopedia Article. Who Is Homological Al Homological algebra. Discussion about Homological algebra. Ecyclopedia or dictionary article about Homological algebra. http://www.knowledgerush.com/kr/encyclopedia/Homological_algebra/

19. Science Fair Projects - Homological Algebra The Ultimate Science Fair Projects Encyclopedia Homological algebra http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Homo

All Science Fair Projects Science Fair Project Encyclopedia for Schools! Search Browse Forum Coach ... Dictionary Science Fair Project Encyclopedia For information on any area of science that interests you, enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.). Or else, you can start by choosing any of the categories below. Science Fair Project Encyclopedia Contents Page Categories Homological algebra Abstract algebra ... 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:

20. Math.com Store: Math Books: Homological Algebra Homological Algebra All Amazon Upgrade - Math Books - Math.com Store the best place to shop for math supplies. http://store.math.com/Books-1000-3540653783-Homological_Algebra.html

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