1. 18: Category Theory, Homological Algebra While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in http://www.math.niu.edu/~rusin/known-math/index/18-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 18: Category theory, homological algebra Introduction Category theory, a comparatively new field of mathematics, provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology. History A survey article which discusses the roles of categories and topoi in twentieth-century mathematics. Applications and related fields The word "category" is used to mean something completely different in general topology Subfields General theory of categories and functors Special categories Categories and algebraic theories Categories with structure Abelian categories Categories and geometry Homological algebra, see also 13DXX, 16EXX, 55UXX This is among the smaller areas in the Math Reviews database. Browse all (old) classifications for this area at the AMS.

2. Lee Lady: HOMOLOGICAL ALGEBRA A Course in homological algebra. Professor EL Lady. University of Hawaii. In the fall University of Hawaii. Books on homological algebra. http://www.math.hawaii.edu/~lee/homolog/

A Course in Homological Algebra Professor E.L. Lady University of Hawaii In the fall of 1974, I returned to the University of Kansas after spending a year at the University of Illinois. During my time at Illinois, I had sat in on a course on Topos Theory (the most avant-garde form of category theory) given by John Gray, and had also attended the commutative ring theory seminars led by Robert Fossum, Philip Griffith, and Graham Evans. I had also spent a lot of time in the library, as usual reading on a large variety of topics, but most especially trying to understand the most recent commutative ring theory, especially as it related to algebraic geometry. Back at Kansas, the ring theorists were concerning themselves with the Gilmer-style theory of non-noetherian commutative rings, and were intimidated by any homological approach at all, even the bare mention of Ext. Paul Conrad who was the head of the algebra department (as it were) at Kansas suggested that I might like to teach a two-semester graduate topics course. I suggested that Homological Algebra might be an appropriate course. My objective was to educate the faculty as well as whatever students enrolled. And in fact, all three rings theorists Brewer, Rutter, and Philip Montgomery, attended regularly.

3. History Of Homological Algebra, By Chuck Weibel History of homological algebra, by Chuck Weibel. This is a survey of the history of homological algebra, from its beginnings with Riemann and Betti, and Poincaré, to http://www.math.uiuc.edu/K-theory/0245

History of Homological Algebra, by Chuck Weibel 0245.bib (222 bytes) survey.dvi (196004 bytes) [December 24, 1997] survey.dvi.gz (85978 bytes) survey.ps.gz (173423 bytes) Chuck Weibel

4. Homological Algebra homological algebra (MAS 6396) Tuesday and Thursday, 1400 1520 p.m., SE 215 Instructor Markus Schmidmeier. Spring 2001. homological algebra (MAS 6396) Often homological algebra is considered as a tool that provides a unified language to problems in various http://www.math.fau.edu/Schmidme/homology.html

Department of Mathematical Sciences Instructor: Markus Schmidmeier Spring 2001 Homological Algebra (MAS 6396) Tuesday and Thursday, 14:00 - 15:20 p.m., SE 215 Often Homological Algebra is considered as a tool that provides a unified language to problems in various fields in Algebra and in Algebraic Topology and that offers various kinds of constructions which are helpful in proofs (e.g. the ``Diagram Chasing''). The focus of this course is on applications: We introduce homological methods (of course), and see how they work in the context of linear algebra problems, like the study of systems of linear maps, or of subspace problems. Preliminaries: Matrix Theory Topics: Categories and functors, projective objects and projective presentations, the Ext-functor, semisimple and hereditary rings, duality and transpose, source maps and sink maps, Auslander-Reiten quivers. Here is a part of my manuscript for downloading: Section 1: k-categories ( dvi ps ), 1/10/01, Section 2: Equivalence and Duality ( dvi ps , Section 3: Abelian Categories dvi ps Section 4: Projective Objects dvi ps Section 5: The Transpose ( dvi ps Section 6: Finite Representation Type ( dvi ps Literature: The following books on Homological Algebra, some taken from our library, can be found in my office (come and read ! ). I intend to use the book by Auslander, Reiten and Smaloe for part of the course as a textbook.

5. Homological Algebra Documentation. Mathematica. The Mathematica Book. Formula Gallery. Diagram from homological algebra (TraditionalForm) ©. 2004 Wolfram Research, Inc. Sign up for our newsletter http://documents.wolfram.com/v4/MainBook/G.1.11.html

PreloadImages('/common/images2003/btn_products_over.gif','/common/images2003/btn_purchasing_over.gif','/common/images2003/btn_services_over.gif','/common/images2003/btn_new_over.gif','/common/images2003/btn_company_over.gif','/common/images2003/btn_webresource_over.gif'); Mathematica 4 Documentation All of Documentation Center All of wolfram.com Documentation Mathematica The Mathematica Book Formula Gallery Diagram from homological algebra (TraditionalForm) Sign up for our newsletter:

6. AC Commutative Algebra Articles cover commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics. http://front.math.ucdavis.edu/math.AC

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ AC Commutative Algebra Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 4 Jun math.AC/0406057 Gorenstein projective dimension for complexes. Oana Veliche AC RA 28 May math.AC/0405526 Semi-dualizing modules and related Gorenstein homological dimensions. Henrik Holm , Peter Jorgensen . 25 pages. AC 28 May math.AC/0405523 Cohen-Macaulay injective, projective, and flat dimension. Henrik Holm , Peter Jorgensen . 18 pages. AC 27 May math.AC/0405499 Associated primes and cofiniteness of local cohomology modules. Mohammad T. Dibaei , Siamak Yassemi . 9 pages. AC Cross-listings 28 May math.AT/0405525 Andrew Baker , Birgit Richter . 6 pages. Glasgow University Mathematics Department preprint no. 04/20. AT AC 27 May math.CV/0405491 La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes. Martin Weimann . 33 pages. CV AC 27 May math.CO/0405490 The ring of multisymmetric functions. F. Vaccarino . 12 pages. CO AC RT 25 May math.AG/0405464 Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz fnctions. Holger Brenner , Georg Hein AG AC Revisions 2 Jun math.AC/0405499

7. Books On Homological Algebra Books on homological algebra. Hilton and Stammbach, A Course in homological algebra (Springer Graduate Texts in Mathematics). This http://www.math.hawaii.edu/~lee/homolog/books-homolog.html

Books on Homological Algebra Hilton and Stammbach, A Course in Homological Algebra (Springer Graduate Texts in Mathematics) This was the nominal text for the course here. I chose it because it was paperbound, and I thought it would be a good reference for students to own. It's a good textbook. Joseph Rotman, Notes on Homological Algebra This was probably the main model I used for the course. Northcott, Introduction to Homological Algebra This was the first book on homological algebra I ever read, before I started graduate school. It is one of the most readable texts available, although some of the notation and terminology is now slightly out of date. MacLane, Homology An excellent reference, and moderately readable. The title is misleading, since no topological aspects of homology are treated at all. Cartan and Eilenberg, Homological Algebra This was the book that started the whole subject, of course. I remember how fascinated I was when I first saw it, since it seemed intriguing that one could apply topology to algebra. I wouldn't recommend that anyone start with this one, but I actually found a number of useful facts here. It should definitely not be considered obsolete.

8. CT Category Theory Section of the eprint arXiv dealing with category theory, including such topics as enriched categories, topoi, abelian categories, monoidal categories, homological algebra. http://front.math.ucdavis.edu/math.CT

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ CT Category Theory Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 4 Jun math.CT/0406061 Tours de torseurs, geometrie differentielle des suites de fibres principaux, et theorie des cordes. Aristide Tsemo CT 13 May math.CT/0405226 Deformation theory of abelian categories. Wenty T. Lowen , Michel Van den Bergh . 44 pages. CT KT 23 Apr math.CT/0404405 Deligne Localized Functors. Maurizio Cailotto . 23 pages. CT AG 23 Apr math.CT/0404399 Isomorphisms in pro-categories. J. Dydak , F. R. Ruiz del Portal CT AT Cross-listings 3 Jun math.GR/0406044 On the Zappa-Szep Product. Matthew G. Brin . 29 pages. GR CT 28 May math.QA/0405517 Fiber Functors on Temperley-Lieb Categories. Yamagami Shigeru . 19 pages. QA CT 25 May math.AG/0405453 Michel Hickel . 45 pages. AG CT 13 May math.KT/0405227 Hochschild cohomology of abelian categories and ringed spaces. W. T. Lowen , M. Van den Bergh . 38 pages. KT CT 30 Apr math.RA/0404522 Algebra generators and information theory. T. Kopf , R. Otahalova . 5 pages. RA CT 29 Apr math.QA/0404504 An analogue of Radford's S^4 formula for finite tensor categories. Pavel Etingof , Dmitri Nikshych , Viktor Ostrik . 14 pages. QA CT 28 Apr math.AT/0404470

9. Cartan, H. And Eilenberg, S.: Homological Algebra (PMS-19). of the book homological algebra (PMS19) by Cartan, H. and Eilenberg, S., published by Princeton University Press of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made...... http://www.pupress.princeton.edu/titles/250.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Homological Algebra (PMS-19) Henri Cartan and Samuel Eilenberg Shopping Cart Table of Contents When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

10. Homological Algebra -- From MathWorld Algebra homological algebra Algebra Named Algebras Miscellaneous Algebras. homological algebra. Modules are the basic tools used in homological algebra. http://mathworld.wolfram.com/HomologicalAlgebra.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Algebra Homological Algebra Algebra ... Miscellaneous Algebras Homological Algebra An abstract algebra concerned with results valid for many different kinds of spaces Modules are the basic tools used in homological algebra. Commutative Diagram Diagram Chasing Diagram Lemma Module ... search Enochs, E. E. and Jenda, O. M. G. Relative Homological Algebra. Berlin: de Gruyter, 2000. Hilton, P. and Stammbach, U. A Course in Homological Algebra, 2nd ed. New York: Springer-Verlag, 1997. Weibel, C. A. An Introduction to Homological Algebra. New York: Cambridge University Press, 1994. Eric W. Weisstein. "Homological Algebra." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/HomologicalAlgebra.html Wolfram Research, Inc.

11. Charles A. Weibel: Home Page Rutgers. Algebraic Ktheory, homological algebra. On-line texts and notes in algebra, history; journal information. http://math.rutgers.edu/~weibel/

Charles Weibel's Home Page The 2004 Almgren "Mayday" Race was held on Sunday May 2. This is an annual relay race between Princeton and Rutgers. Teaching Stuff (for more information, see Rutgers University , the Rutgers Math Department , and its Graduate Math Program My schedule (Addresses, courses, office hours) Statistical evidence for the effectiveness of our Calculus Workshop formats Statistical evidence for the effectiveness of web-based homework in Calculus Undergraduate Course Materials , as well as course material for Calculus I (Math 135) and WeBWork Calculus II for the Biological Sciences (Math 138) Cryptography (Math 348) Spring 2004 ( homework Graduate Algebra Supplementary Materials Bilinear forms supplement and the Group representations supplement Research stuff: Here are some research papers my research interests and my Ph.D. Students Corrections to my textbook ``An introduction to homological algebra'' Chapters in my book-in-progress ``Algebraic K-theory'' Lectures on motivic cohomology (Beta version) Thomason Obituary Material (photos and articles) Do you like the History of Mathematics?

12. Commutative Algebra: Interactions With Homological Algebra And Representation Th Calendar. Commutative Algebra Interactions with homological algebra and Representation Theory. February 3, 2003 to February 7, 2003. http://zeta.msri.org/calendar/workshops/WorkshopInfo/199/show_workshop

Calendar Commutative Algebra: Interactions with Homological Algebra and Representation Theory February 3, 2003 to February 7, 2003 Organized by: Luchezar Avramov (chair), Ragnar Buchweitz, and John Greenlees Recently, commutative algebra has been developing new connections with a variety of fields, and adding new directions to some traditional links. This interdisciplinary workshop proposes to generate an active exchange of information between practitioners and consumers of commutative algebra. The subjects discussed will include invariant theory, cohomology of groups, free resolutions, rational homotopy, stable homotopy, representation theory, and derived categories. The following have accepted invitations to speak: W. Bruns J. Carlson H. Derksen W. Dwyer H.-B. Foxby J. Herzog C. Huneke S. Iyengar G. Lyubeznik M. Neusel I. Reiten J. Rickard P. Roberts J.-E. Roos B. Shipley K. Smith M. Van der Bergh J. Weyman R. Wiegand S. Yuzvinski Commutative Algebra: Interactions with Homological Algebra and Representation Theory Schedule Parent Program: Commutative Algebra Lectures on Streaming Video: This event is now over. Resources from this event, including

13. Commutative Algebra: Interactions With Homological Algebra And Representation Th Commutative Algebra Interactions with homological algebra and Representation Theory. February 3, 2003 to February 7, 2003 http://www.msri.org/calendar/workshops/WorkshopInfo/199/show_workshop

Calendar Commutative Algebra: Interactions with Homological Algebra and Representation Theory February 3, 2003 to February 7, 2003 Organized by: Luchezar Avramov (chair), Ragnar Buchweitz, and John Greenlees Recently, commutative algebra has been developing new connections with a variety of fields, and adding new directions to some traditional links. This interdisciplinary workshop proposes to generate an active exchange of information between practitioners and consumers of commutative algebra. The subjects discussed will include invariant theory, cohomology of groups, free resolutions, rational homotopy, stable homotopy, representation theory, and derived categories. The following have accepted invitations to speak: W. Bruns J. Carlson H. Derksen W. Dwyer H.-B. Foxby J. Herzog C. Huneke S. Iyengar G. Lyubeznik M. Neusel I. Reiten J. Rickard P. Roberts J.-E. Roos B. Shipley K. Smith M. Van der Bergh J. Weyman R. Wiegand S. Yuzvinski Commutative Algebra: Interactions with Homological Algebra and Representation Theory Schedule Parent Program: Commutative Algebra Lectures on Streaming Video: This event is now over. Resources from this event, including

14. Homological Algebra Over Cohen-Macaulay Rings Calendar. homological algebra over CohenMacaulay rings. Parent Workshop Commutative Algebra Interactions with homological algebra and Representation Theory. http://zeta.msri.org/calendar/talks/TalkInfo/1751/show_talk

Calendar Homological algebra over Cohen-Macaulay rings Craig Huneke (Scheduled Workshop Talk) Monday, Feb 3, 2003 9:30 am to 10:25 am at the MSRI Lecture Hall, Mathematical Sciences Research Institute, Berkeley, California In this talk, I will describe several problems (and some solutions) dealing with the vanishing of Tor and Ext over Cohen-Macaulay rings. The talk will discuss some work with Graham Leuschke on rings of finite CM type, as well as work in progress with Graham Leuschke and also Liana Sega and Adela Vraciu. The basic question of the talk is the following: let R be a Cohen-Macaulay local ring and let M and N be finitely generated R-modules. When do all large Tor(M,N) or Ext(M,N) vanish? What do these condition mean? The talk will also focus on the case of a domain R of positive characteristic p over a perfect field, and discuss some known results concerning the decomposition of the p^nth roots of R into indecomposable R-modules. Parent Workshop: Commutative Algebra: Interactions with Homological Algebra and Representation Theory MSRI Home Page Search the MSRI Website Subject and Title Index ... webmaster@msri.org

15. Courses homological algebra ps file (479K) homological algebra - pdf file (228K) is a very short introduction to local fields and local class field theory without using homological algebra http://www.maths.nottingham.ac.uk/personal/ibf/courses.html

Lecture Notes of Courses (.ps and .pdf files) Introduction to number theory - ps file (495K) Introduction to number theory - pdf file (242K) This is a first course in number theory. It includes p-adic numbers. Commutative algebra - ps file (381K) Commutative algebra - pdf file (202K) This course is an introduction to categories, modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization. Introduction to algebraic number theory - ps file (432K) Introduction to algebraic number theory - pdf file (193K) This course (36 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding. Integrality over rings, algebraic extensions of fields, field isomorphisms, norms and traces are discussed in the second part. Dedekind rings, factorization in Dedekind rings, norms of ideals, splitting of prime ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated in the second part. Homological algebra - ps file (479K) Homological algebra - pdf file (228K) This is a very short introduction to homological algebra This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.

16. Math 406 Homological Algebra University of Illinois at UrbanaChampaign Math 406 homological algebra Spring 1999. Professor J. Rotman 1000 am, MWF 443 Altgeld Hall. http://www.math.uiuc.edu/Classes/math406.html

Math 406 Homological Algebra Spring 1999 Professor J. Rotman 10:00 a.m., M W F 443 Altgeld Hall The course will construct the functors Ext and Tor on categories of R-modules, where R is a ring. We will begin with projective, injective, and flat resolutions and derived functors. Various dimensions of modules and of rings will be discussed, and applications will focus on rings and cohomology of groups (once some version of homological algebra is learned, applications to other areas, e.g. Lie algebras or sheaves, are routine). The course will end with a discussion of spectral sequences (via exact couples) and more applications to rings and groups. Although the origins of homological algebra are in Algebraic Topology, we will not assume familiarity with homology and cohomology of spaces. Prerequisite: Math 402 References: Rotman, Introduction to Homological Algebra Cartan-Eilenberg, Homological Algebra Mac Lane, Homology Weibel, Introduction to Homological Algebra Weiss, Cohomology of Groups Please send additions to the webmaster of this page.

17. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. Category Theory, homological algebra Dave Rusin; The Mathematical Atlas have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of http://mathforum.com/library/topics/category_theory

Browse and Search the Library Home Math Topics Algebra Modern Algebra : Cat. Theory/Homolgcl Alg. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Category Theory, Homological Algebra - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to category theory, a comparatively new field of mathematics that provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 19 items found, showing 1 to 19 Applied and Computational Category Theory - RISC-Linz, Austria A brief history and description of category theory, and some related links. From the Research Institute for Symbolic Computation. ...more>> Categories, Quantization, and Much More - John Baez

18. Cartan, H. And Eilenberg, S.: Homological Algebra (PMS-19). of the book homological algebra (PMS19) by Cartan, H. and Eilenberg, S., published by Princeton University Press. homological algebra (PMS-19)....... http://pup.princeton.edu/titles/250.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Homological Algebra (PMS-19) Henri Cartan and Samuel Eilenberg Shopping Cart Table of Contents When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

19. Buy Basic Homological Algebra By M. Scott Osborne At Walmart.com Basic homological algebra by M. Scott Osborne in Hardcover. ISBN 038798934X. This is a foundational book on homological algebra. It covers Ext and Tor early and without distraction, and includes http://rdre1.inktomi.com/click?u=http://na.link.decdna.net/n/3532/4200/www.walma

20. Non-abelian Homological Algebra Last updated 21 January, 1999. Some publications in nonabelian homological algebra. This Bibliography lists some papers and books http://www.bangor.ac.uk/~mas010/nonlnpub.htm

Last updated 21 January, 1999 Some publications in non-abelian homological algebra This Bibliography lists some papers and books on multiple categories and groupoids, non-linear homological algebra, and related areas directly relevant to the themes developed in the accompanying article on Higher dimensional group theory The list is not complete, and should be thought of more as an entry point into the literature. It is hoped to develop it over time. The paper "Some problems in non abelian homological and homotopical algebra" gives some 35 problems or problem areas in this field. I have given a separate and fuller bibliography on the non abelian tensor product. This bibliography should be related to papers on Lie groupoids, Lie algebroids and Lie pseudoalgebras in a bibliography compiled by Kirill Mackenzie. Papers added in 2004 are coloured brown. R.Aboughazi, `Produit tensoriel du groupe d'Heisenberg', Bull. Soc. Math. France, 15, 95-106, 1987. G. Abramson, J.-P.Meyer, J.Smith, `A higher dimensional analogue of the fundamental groupoid', in Recent developments of algebraic topology, RIMS Kokyuroku 781, Kyoto, 38-45, 1992. F.Al-Agl, Aspects of multiple categories, University of Wales PhD Thesis, 1989.

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