1. 18: Category Theory, Homological Algebra There are a number of textbooks on homological algebra which should be accessible to graduate homological algebra, by Henri Cartan and Samuel Eilenberg. 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. 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 2005 Almgren "Mayday" Race was held on Sunday May 1. There were eight teams, and the winner was the Rutgers Physics team, with a time of 3:00. 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 Thomason Obituary Material (photos and articles) Do you like the History of Mathematics?

3. Lee Lady HOMOLOGICAL ALGEBRA Lee Lady Topics in homological algebra http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. 55: Algebraic Topology Homological methods are used throughout algebra. While primarily a direct application of homological algebra, these are indirectly related to topology (eg http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 55: Algebraic topology Introduction Algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fiber bundles and related spaces are included here, while complexes (CW-, simplicial-, ...) are treated in section 57. Finally, the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences; the machinery (mostly derived from homological algebra) is powerful if rather daunting. In all cases, the "naturality" of the construction implies that a map between spaces induces a map between the groups. Thus one can show that no maps of some sort can exist between two spaces (e.g. homeomorphisms) since no corresponding group homomorphisms can exists. That is, the groups and homomorphisms offer an algebraic "obstruction" to the existence of maps. Classic applications include the nonexistence of retractions of disks to their boundary and, as a consequence, the Brouwer Fixed-Point Theorem. (Obstruction theory is, more generally, the creation of algebraic invariants whose vanishing is necessary for the existence of certain topological maps. For example a function defined on a subspace Y of a space X defines an element of a homology group; that element is zero iff the function may be extended to all of X.)

5. Arxiv AC Commutative Algebra Articles cover commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Homological Algebra -- From MathWorld Modules are the basic tools used in homological algebra. SEE ALSO Commutative Diagram, Enochs, EE and Jenda, OMG Relative homological algebra. http://mathworld.wolfram.com/HomologicalAlgebra.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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. SEE ALSO: Commutative Diagram Diagram Chasing Diagram Lemma Module ... [Pages Linking Here] 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. CITE THIS AS: Eric W. Weisstein. "Homological Algebra." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/HomologicalAlgebra.html Wolfram Research, Inc.

7. 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 16 Sep 2005 Search Submit Retrieve Subscribe ... iFAQ AC Commutative Algebra Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 16 Sep math.AC/0509340 Finiteness of extension functors of local cohomology modules. Mohammad T. Dibaei , Siamak Yassemi . 5 pages. AC AG 13 Sep math.AC/0509247 Truncated Groebner fans and lattice ideals. Niels Lauritzen AC AG CO 12 Sep math.AC/0509209 Combinatorial shifting and graded Betti numbers. Satoshi Murai , Takayuki Hibi AC CO 9 Sep math.AC/0509186 A general framework for applying FGLM techniques to linear codes. M. Borges-Quintana , M. A. Borges-Trenard , E. Martinez-Moro AC CO 9 Sep math.AC/0509180 Power series rings and projectivity. R. O. Buchweitz , H. Flenner . 6 pages. AC Cross-listings 14 Sep math.AG/0509285 The Multiplicity Polar Theorem and Isolated Singularities. Terence Gaffney . 22 pages. AG AC 14 Sep math.AG/0509282 A Briancon-Skoda type theorem for graded systems of ideals. Alex Kuronya , Alexandre Wolfe . 8 pages. AG AC 13 Sep math.AG/0509243 On Igusa zeta functions of monomial ideals. Jason Howald , Mircea Mustata , Cornelia Oichi Yuen . 9 pages. AG AC 9 Sep math.AT/0509187

8. CT Category Theory Section of the eprint arXiv dealing with category theory, including such topics as enriched categories, topoi, abelian categories, monoidal http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Homological Algebra -- From MathWorld Cofree Module homological algebra Ring Regular Sequence Cokernel Homology Serre s Conjecture Colimit Homology Boundary Short Exact Sequence http://mathworld.wolfram.com/topics/HomologicalAlgebra.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Algebra Homological Algebra Alternating Algebra Exact Functor Module Direct Sum Artinian Module ... Module

10. 18 Category Theory, Homological Algebra 18 Category theory, homological algebra http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Lee Lady: HOMOLOGICAL ALGEBRA Lee Lady Topics in homological algebra. I suggested that homological algebra might be an appropriate course. My objective was to educate the faculty as 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.

12. Chuang, Joe University of Bristol. Representation theory of finite groups, homological algebra. Teaching resources. http://www.maths.bris.ac.uk/~majc/

Joe Chuang's Home Page Lecturer in Pure Mathematics Office: 3.8 Tel. (0117)9289126 E-mail address: Joseph.Chuang@bristol.ac.uk School of Mathematics, University of Bristol Clifton, Bristol, AVON, BS8 1TW, UK Mathematics 1AM: Multivariable Calculus Problem Sheets: Solutions: 1 (without drawings) 1 (with drawings) Some notes: Sections 0-2 (pp.1-10) Section 3 (pp.11-17) Section 4 (pp.18-24) Sections 5-6 (pp.25-30) ... Figures for Sections 7-8 Assignment history: 16 Feb. PS1: #1,2,4ab. 23 Feb. PS1: #6a; PS2: #1,5,9a. 2 Mar. PS2: #3,6,8; PS3: #1,3. 9 Mar. PS3: #4; PS4: #1a,2,5ab,6. 16 Mar. PS4: #4,7; PS5: #1,5. 20 Apr. PS5: #6,7; PS6: #1,2,3. 27 Apr. PS7: all questions. Algebraic Toplogy Lecture notes (and some corrections to the notes) Problem Sheets: Solutions: Graduate students Michael Peach's PhD Thesis dvi pdf Back to Pure Group Home Page. Back to Department of Mathematics Home Page.

13. Algebraic Areas Of Mathematics a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Books On Homological Algebra Hilton and Stammbach, A Course in homological algebra (Springer Graduate Texts in This was the first book on homological algebra I ever read, 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.

15. 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 16 Sep 2005 Search Submit Retrieve Subscribe ... iFAQ CT Category Theory Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 15 Sep math.CT/0509318 Lambda-presentable morphisms, injectivity and (weak) factorization systems. Michel Hebert . 16 pages. CT 14 Sep math.CT/0509266 2-C*-categories with non-simple units. Pasquale A. Zito . 47 pages. CT OA 6 Sep math.CT/0509102 Notes on enriched categories with colimits of some class (completed version). G. M. Kelly , V. Schmitt CT 6 Sep math.CT/0509056 On lifting diagrams up to homotopy in Frobenius categories. Matthias Kuenzer CT 30 Aug math.CT/0508565 A definition of triangulated categories following Heller. Matthias Kuenzer CT KT 25 Aug math.CT/0508479 Quotients of Tannakian Categories. J. S. Milne CT AG 23 Aug math.CT/0508379 Support varieties - an ideal approach. Aslak Bakke Buan , Henning Krause Solberg . 25 pages. CT AG RT Cross-listings 31 Aug math.GR/0508617 A simple description of Thompson's group F. Marcelo Fiore , Tom Leinster . 14 pages. GR CT 29 Aug math.LO/0508531 Models of Non-Well-Founded Sets via an Indexed Final Coalgebra Theorem. Benno van den Berg , Federico De Marchi LO CT 23 Aug math.AT/0508416

16. Mathematics Archives - Topics In Mathematics - Abstract Algebra A Course in homological algebra. Course Notes J.S. Milne ADD. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. 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

18. Jeremy Rickard's Home Page University of Bristol. Modular representation theory of finite groups and related areas of algebraic topology; homological algebra; Representation theory of finitedimensional algebras. Publications, resources. http://www.maths.bris.ac.uk/~majcr/

Jeremy Rickard's Home Page Professor of Pure Mathematics Office: 3.4 Tel: (0117) 928 7989 Fax: (0117) 928 7999 School of Mathematics University of Bristol University Walk Bristol BS8 1TW UK Research interests Modular representation theory of finite groups and related areas of algebraic topology. Homological algebra. Representation theory of finite-dimensional algebras. Teaching 2003-2004 Representation Theory (Level 4, 1st semester): Unit Description Home page Core Mathematics B (Linear Algebra) (Level 1, weeks 13-24): Unit Description Home page Research Some of my recent publications and preprints. Links Some useful links. LMS Durham Symposium: Representations of Finite Groups and Related Algebras (1-11 July 2002) Mail me: Pure Mathematics Group Home Page Mathematics Department Home Page University of Bristol Home Page

19. Peter Jorgensen's Homepage Peter Jorgensen's homepage. I am a mathematician whose primary interests are homological algebra and homotopical algebra. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. Relative Homological Algebra For The Proper Class Omega_f, By Grigory Garkusha Relative homological algebra for the proper class omega_f, by Grigory Garkusha. This paper has been updated again by the author. http://www.math.uiuc.edu/K-theory/0479/

Relative homological algebra for the proper class omega_f, by Grigory Garkusha [This paper has been updated again by the author.] First version: Apr 22, 2001; second version: Jul 23, 2001; third version: Nov 13, 2002. 0479.bib (253 bytes) ASIAN11.dvi (121020 bytes) [November 13, 2002] ASIAN11.dvi.gz (45137 bytes) ASIAN11.ps.gz (117948 bytes) Grigory Garkusha

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