1. 18: Category Theory, Homological Algebra In the "known maths" series.Category Science Math Algebra Category Theory...... While the general theory and certain types of categories have attracted considerableinterest, 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 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. Textbooks, reference works, and tutorials

2. Lee Lady: HOMOLOGICAL ALGEBRA Lee Lady Topics in homological algebra A Course in homological algebra. Professor E.L. 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. Non-abelian Homological Algebra Last updated 21 January, 1999 Some publications in nonabelian homological algebra R.Brown, `Some problems in non-Abelian homological and homotopical algebra', Homotopy theory and related topics 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. 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.

4. 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 the previous decade. 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

5. An Introduction To Homological Algebra - Cambridge University Press A portrait of the subject of homological algebra as it exists today. The landscape of homological algebra has evolved over the last halfcentury into a fundamental tool for the working http://books.cambridge.org/0521559871.htm

Home Catalogue Related Areas: Pure Mathematics Cambridge Studies in Advanced Mathematics New titles Email For updates on new titles in: Pure Mathematics An Introduction to Homological Algebra Charles A. Weibel Hardback In stock Contents 1. Chain complexes; 2. Derived functors; 3. Tor and Ext; 4. Homological dimensions; 5. Spectral sequences; 6. Group homology and cohomology; 7. Lie algebra homology and cohomology; 8. Simplicial methods in homological algebra; 9. Hothschild and cyclic homology; 10. The derived category; Appendix: category theory language. Cambridge University Press 2001. Security Order by phone (+44 (0)1223 326050) or fax (+44 (0)1223 326111).

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

Tue 18 Mar 2003 Search Submit Retrieve Subscribe ... iFAQ AC Commutative Algebra Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 18 Mar math.AC/0303200 Valuations, Deformations, and Toric Geometry. Bernard Teissier AC AG 14 Mar math.AC/0303151 Rank one Maximal Cohen-Macaulay modules over singularities of type Y_1^3+Y_2^3+Y_3^3+Y_4^3. Viviana Ene , Dorin Popescu AC 13 Mar math.AC/0303139 Minimal Hilbert-Kunz multiplicity. Kei-ichi Watanabe (Nihon University), Ken-ichi Yoshida (Nagoya University). 22 pages. AC 13 Mar math.AC/0303134 "Geometric quotients are algebraic schemes" based on Fogarty's idea. Mitsuyasu Hashimoto . 9 pages. AC AG Cross-listings 18 Mar math.AG/0303203 Multiplier Ideals of Sufficiently General Polynomials. Jason Howald . 9 pages. AG AC 18 Mar math.AG/0303189 Log-terminal singularities and vanishing theorems. Hans Schoutens AG AC RA 18 Mar math.GR/0303187 Dickson invariants, regularity and computation in group cohomology. David Benson GR AC RA 14 Mar math.AT/0303164 Stanley-Reisner rings and torus actions. Taras E. Panov (Moscow State University and ITEP). 28 pages. ITEP-TH-91/02. AT AC CO 13 Mar math.AG/0303148

7. MATH 620 Proposal This is the outline of a proposed course in homological algebra. MATH 620homological algebra. DATE Fall Term, 2003. INSTRUCTOR John Beachy. http://www.math.niu.edu/~beachy/courses/algebra/03f620proposal.html

This is the outline of a proposed course in homological algebra. Please note that in the graduate catalog this course is listed as Math 522, but there has been interest in offering it at the 600 level. MATH 620: HOMOLOGICAL ALGEBRA DATE: Fall Term, 2003 INSTRUCTOR: John Beachy COURSE DESCRIPTION: Categories and functors, projective and injective modules, complexes and homology, Ext, Tor, and dimensions. Applications to cohomology of groups and ring theory. PREREQUISITE: MATH 521 TEXT: An Introduction to Homological Algebra, by Rotman [Academic Press, 1979] SYLLABUS: Chapter 1: Introduction Some history and motivating problems; categories and functors; tensor products Chapter 2. Hom and tensor Direct sums and products; exact sequences; adjoint functors; direct and inverse limits Chapter 3. Projectives, injectives, and flats Modules: free, projective, injective, and flat Extensions of modules Notes on n-fold extensions of modules Chapter 6: Homology Homology functors; derived functors Chapter 7: Ext The functor Ext and its relation to extensions of modules Chapter 8: Tor The functor Tor and its relation to torsion in modules Unfortunately, it seems to be impossible to also cover several important chapters:

8. Mark McConnell WANDL, Inc. Papers and software for homological algebra. http://www.math.okstate.edu/~mmcconn/

Mark McConnell's Home Page In May 1999, I left academia and took up a new career at WANDL , a small company that produces software for modeling large telecommunications networks. Our family's home is in Warren, NJ. My daughter and I are members of the choir of Trinity Episcopal Church in Princeton. Here is my original home page , with information about my mathematical work, my program Sheafhom , musical activities, family, etc. Our current contact information is: Mark McConnell and Connie Chen 27 Wolf Hill Dr. Warren, NJ 07059-5327 (908) 542-9851 (home) (732) 868-0100 ext. 235 (work) mmcconnell@wandl.com

9. Grundkurser I Matematik & Tillämpad Matematik / Numerisk Analys Rotman, An Introduction to homological algebra, Academic Press. Gavs senast i lp http://www.math.chalmers.se/Math/Foutb/Grundkurser.html

Matematiska institutionen Utbildning Forskarutbildning Grundkurser inom forskarutbildningen Kurserna är indelade i följande grupper: [A] Algebra [B] Topologi [C] Analys Litteraturuppgifterna nedan avser standardlitteraturen, och det händer att annan litteratur används. [A] Algebra [A1] Galoisteori (5p) Ändliga kroppsutvidgningar, Galoisgrupper, lösbarhet av polynomekvationer Litteratur: I.N. Stewart, Galois Theory Ges vartannat år; gavs senast i lp II 1995/96 av Juliusz Brzezinski [A2] Algebraisk talteori (5p) Algebraiska tal, Dedekindringar, kvadratiska och cyklotomiska kroppar, geometriska metoder, klassgrupper, Dirichlets enhetssats, diofantiska ekvationer, lokala och analytiska metoder Litteratur: I. Stewart, D. Tall, Algebraic number theory Number Fields , Springer, eller J.P. Serre, A Course in Arithmetic , Springer Ges vartannat år; gavs senast i lp II 1996/97 av Juliusz Brzezinski [A3] Grundkurs i algebra / Algebra för doktorander, I (5p) Moduler över ringar, multilinjär algebra, bilinjära och seskvilinjära former, Cliffordalgebror, klassiska grupper, kanoniska former av tensorer (Jordans normalform), kategorier och funktorer, halvenkelhet och grupprepresentationer, Liealgebror Litteratur: S. Lang

10. Books On Homological Algebra Books on homological algebra. Hilton and Stammbach, A Course in HomologicalAlgebra (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.

11. 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

Tue 18 Mar 2003 Search Submit Retrieve Subscribe ... iFAQ CT Category Theory Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 17 Mar math.CT/0303175 Categorical and combinatorial aspects of descent theory. Ross Street . 45 pages. CT KT 10 Mar math.CT/0303083 Paracategories I: internal parategories and saturated partial algebras. Claudio Hermida , Paulo Mateus CT 27 Jan math.CT/0301271 Non abelian cohomology: the point of view of gerbed tower. Aristide Tsemo . 20 pages. CT 22 Jan math.CT/0301221 The Combinatorics of Iterated Loop Spaces. M. A. Batanin . 23 pages. CT AT Cross-listings 18 Mar math.FA/0303186 Very badly approximable matrix functions. V. V. Peller , S. R. Treil . 27 pages. FA CA CO CT ... CV 6 Mar math.KT/0303050 N-Fold Cech Derived Functors and Generalised Hopf type formulas. Guram Donadze , Nick Inassaridze , Timothy Porter . 30 pages. KT CT 5 Mar math.AG/0303037 Derived categories of cubic and V14 threefolds. Alexander Kuznetsov . 24 pages. AG CT 26 Feb math.AG/0302304 Triangulated categories of singularities and D-branes in Landau-Ginzburg models. Dmitri Orlov . 29 pages. AG CT 25 Feb math.AT/0302284

12. Commutative Algebra: Interactions With Homological Algebra And Representation Th Calendar. Commutative Algebra Interactions with homological algebraand 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

13. 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 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) Math. Theory of Probability Cryptography (Math 395) Spring 2003 ( homework and department's 395 course page 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?

14. Commutative Algebra: Interactions With Homological Algebra And Representation Th Sheafhom is a set of programs I'm developing for homological algebra and algebraic topology. 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

15. Homological Algebra Over Cohen-Macaulay Rings Calendar. homological algebra over CohenMacaulay rings. Parent Workshop CommutativeAlgebra Interactions with homological algebra and Representation Theory. http://www.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

16. Homological Algebra HeisenbergEuler Lagrangian Zeta Function Sums. Diagram from homological algebra(TraditionalForm). Heisenberg-Euler Lagrangian Zeta Function Sums. http://documents.wolfram.com/v4/MainBook/G.1.11.html

Documentation Mathematica The Mathematica Book Formula Gallery All Documentation Mathematica 4 Documentation The Mathematica Book Built-in Functions Getting Started Add-ons ... For More Information Diagram from homological algebra (TraditionalForm) Please send comments and suggestions about this web site to docucenter@wolfram.com

17. Wolfram Research, Inc. Tour of Features. Key Elements of Mathematica. Upgrades. For More Information. Diagramfrom homological algebra (TraditionalForm), © 2003 Wolfram Research, Inc. http://documents.wolfram.com/v3/MainBook/G.1.11.html

Documentation Mathematica The Mathematica Book Formula Gallery ... For More Information Diagram from homological algebra (TraditionalForm) Please send comments and suggestions about this web site to docucenter@wolfram.com

18. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. sites and Web pages relating to the study of mathematics. This pagecontains sites relating to Category Theory/homological algebra. http://mathforum.org/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

19. About "A Course In Homological Algebra" A Course in homological algebra. Library Home Full Table of Contents Suggesta Link Library Help Math Topics Category Theory/homological algebra. http://mathforum.org/library/view/6845.html

A Course in Homological Algebra Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.math.hawaii.edu/~lee/homolog/ Author: E. Lee Lady; University of Hawaii Description: A collection of graduate course notes. Files are in PDF and DVI formats. Contents include: tor, flatness, and purity; syzygies, projective dimension and global dimension; Gorenstein rings and modules; Auslander's proof of Roiter's Theorem; and a list of books on homological algebra. Levels: College Languages: English Resource Types: Course Notes Math Topics: Category Theory/Homological Algebra Suggestion Box Home The Math Library ... Search http://mathforum.org/ webmaster@mathforum.org

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

Algebra Homological Algebra Algebra Named Algebras ... 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 References 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. Author: Eric W. Weisstein Wolfram Research, Inc.

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