21. 18: Category Theory, Homological Algebra In the known maths series. 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.

22. Lee Lady: HOMOLOGICAL ALGEBRA I wanted to teach essentially everything I knew about homological algebra and category theory, with a large dose of the kind of commutative ring theory that http://www.math.hawaii.edu/~lee/homolog/

A Course in Homological Algebra E.L. Lady 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.

23. Homological Algebra -- From Wolfram MathWorld An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra. http://mathworld.wolfram.com/HomologicalAlgebra.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... 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 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: Weisstein, Eric W. "Homological Algebra." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/HomologicalAlgebra.html Contact the MathWorld Team Wolfram Research, Inc. Wolfram Research Mathematica Home Page ... Wolfram Blog

24. HOMOLOGICAL ALGEBRA File Format PDF/Adobe Acrobat Quick View http://www.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/2.Spr

25. Homological Algebra File Format PDF/Adobe Acrobat http://www.cis.upenn.edu/~cis610/alg5.pdf

26. Homological Algebra: Definition From Answers.com The study of the structure of modules, particularly by means of exact sequences; it has application to the study of a topological space via its homology groups. http://www.answers.com/topic/homological-algebra

27. Front: Math.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

Front for the arXiv Fri, 29 Oct 2010 Front math AC search register submit journals ... iFAQ math.AC Commutative Algebra Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 29 Oct arXiv:1010.5952 On Certain Divisibility Property of Polynomials. Luis F. Caceres , Jose A Velez Marulanda math.AC 29 Oct arXiv:1010.5878 Another definition of Euler class group of a Noetherian ring. Manoj K Keshari , Satya Mandal math.AC 28 Oct arXiv:1010.5768 Gröbner bases of contraction ideals. Takafumi Shibuta math.AC 28 Oct arXiv:1010.5704 Type sequences of one-dimensional local analytically irreducible rings. Valentina Barucci , Ioana Cristina math.AC 28 Oct arXiv:1010.5615 Lexsegment ideals are sequentially Cohen-Macaulay. Muhammad Ishaq math.AC 27 Oct arXiv:1010.5480 Continuous closure of sheaves. János Kollár (Princeton Univ). math.AC math.AG 26 Oct arXiv:1010.5066 A Chevalley theorem for difference equations. Michael Wibmer math.AC math.AG 25 Oct arXiv:1010.4692 Values and bounds of the Stanley depth. Muhammad Ishaq math.AC

28. Homological Algebra And ... more details later Tentative outline/list of topics . Notes, examples, supplements (Reverse chronological order. Labels will become links when targets are ready.) http://www.math.umn.edu/~garrett/m/hom/

Homological algebra and ... [ambient page updated Thu, 08 Apr '10, 06:44 PM] ... [ home [more details later...] Tentative outline/list of topics Notes, examples, supplements (Reverse chronological order. Labels will become links when targets are ready.) DeRham, Dolbeault theorems ... Chern classes Cech sheaf cohomology and connection to algebraic topology Presheaves and sheaves, acyclic resolutions, derived-functor sheaf cohomology Universal delta functors Derived functors, projectives, injectives, Baer's criterion exercises/examples: Ext, Tor, group (co-) homology, Lie algebra (co-) homology, local cohomology 03 adjoints, naturality, exactness, small Yoneda lemma 03x exercises/examples: standard adjoint pairs... Hom and tensor, fixed and co-fixed vectors, isotypes and co-isotypes... adjoints to forgetful functors are free objects 02 Yoneda's Ext and extensions 01 Popular categories 00 Introduction and overview 00a naive set theory 00x exercises/examples 00y exercises/examples Sample phenomena illustrating homological ideas in nature: Snake lemma, extensions, Gamma function

29. Getting Comfortable With Homological Algebra Getting comfortable with homological algebra Linear Abstract Algebra discussion http://www.physicsforums.com/showthread.php?t=331469

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

Charles Weibel's Home Page Definition: Proofiness Proofiness. Teaching Stuff (for more information, see Rutgers University , the Rutgers Math Department , and its Graduate Math Program My schedule (Addresses, courses, office hours) Undergraduate Course Materials , as well as course material for Calculus I (Math 135) and WeBWork Graph Theory (Math 428) Fall 2010 Statistical evidence for the effectiveness of our Calculus Workshop formats Statistical evidence for the effectiveness of web-based homework in Calculus Graduate Algebra Supplementary Materials Math 551 course page and Homework Assignments Bilinear forms supplement Group representations supplement This is a link to some of my research papers . Here are my research interests and my Ph.D. Students Fall 2006 Lectures on the proof of the Bloch-Kato Conjecture Corrections to the H-book An introduction to homological algebra , Cambridge Univ. Press, 1994. Lectures on motivic cohomology , Clay Monographs in Math 2 (2006), AMS. Chapters in my K-book ``Algebraic K-theory'' Do you like the History of Mathematics?

31. 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 This paper appeared as pp.797-836 in the book The History of Topology , ed. I.M. James, Elsevier, 1999. 0245.bib (222 bytes) survey.dvi (196004 bytes) [December 24, 1997] survey.dvi.gz (85978 bytes) survey.pdf (339539 bytes) survey.ps.gz (265422 bytes) Chuck Weibel

32. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. 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 http://www.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 - 21 items found, showing 1 to 21 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

33. Grothendieck Circle Aims to make publicly available materials written by and about Alexandre Grothendieck. Made contributions to algebraic geometry, homological algebra and functional analysis. Page includes list of mathematical,biographical publications and some portrait photos. http://people.math.jussieu.fr/~leila/grothendieckcircle/

Mathematical texts Biographical Texts Photograph Album Circle Members URL: www.grothendieckcircle.org The long-term goal of the Grothendieck Circle is to make publicly available (and in some cases translate) published and unpublished material written by (and about) Alexandre Grothendieck, as well as to provide some biographical material. Since many of these texts are unpublished or are out of print, we hope that this site will serve as a valuable resource to researchers, expanding over time. Presently ongoing communication with A. Grothendieck will determine the future of this website Recent additions to the site: A transcription of Illusie's oral reminiscences of his years as a student of Grothendieck has replaced the original audio recording (biographical texts).

34. Homological Algebra Peter Teichner Math 253, Homological Algebra Spring 2008, Tu/Th 111230 in 3 Le Conte Office hour Tuesday 2-3 in 703 Evans. GSR Chris Schommer-Pries, office hour Wednesday 9 http://math.berkeley.edu/~teichner/Courses/253.html

Peter Teichner Math 253, Homological Algebra Spring 2008, Tu/Th 11-12:30 in 3 Le Conte Office hour Tuesday 2-3 in 703 Evans. GSR: Chris Schommer-Pries, office hour Wednesday 9-10 in 1060, discussion session Friday 12-1 in 939 Evans. Please submit the first problem of the following sets in writing, other problems will be discussed during the Friday 12-1 session. Homework 1 , due Friday, Feb. 1 Homework 2 , due Friday, Feb. 8 Homework 3 , due Friday, Feb. 15 Homework 4 , due Friday, Feb. 22 Homework 5 , due Friday, Feb. 29 In each group, please submit different problems in writing during the following weeks. Homework 6 , due Friday, March 7 Homework 7 , due Friday, March 14 Homework 8 , due Friday, March 21 Homework 9 , due Friday, April 4 Homework 10 , due Friday, April 11 Homework 11 , due Friday, April 18 Homework 12 , due Friday, April 25 Homework 13 , due Friday, May 2 The class will start with basic constructions for chain complexes, with an eye towards group cohomology. We'll explain the relation of the first three cohomology groups with extensions of groups and we'll show how group cohomology drastically restricts the class of finite groups that can act freely on spheres. The second part of the class will introduce spectral sequences, a basic tool in all computational aspects of cohomology theory. In the last part of the class we'll study some homotopical algebra, including derived categories and their application. The best way to learn the material in this course is by doing your own diagram chases and guessing your own definitions. That's why we'll have homework problems every week, posted on this website. They will be partially due in writing and partially presented during the discussion hour with Chris.

35. Front: Math.CT Category Theory Section of the e-print 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

Front for the arXiv Fri, 29 Oct 2010 Front math CT search register submit journals ... iFAQ math.CT Category Theory Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 29 Oct arXiv:1010.5934 Touchard like polynomials and generalized Stirling numbers. G. Dattoli , B. Germano , M. R. Martinelli , P. E. Ricci math.CT 27 Oct arXiv:1010.5304 Note on star-autonomous comonads. Craig Pastro math.CT 26 Oct arXiv:1010.4956 Dendroidal Segal spaces and infinity-operads. Denis-Charles Cisinski , Ieke Moerdijk math.CT math.AT 26 Oct arXiv:1010.4819 On the Cohomology Comparison Theorem. Alin Stancu math.CT 22 Oct arXiv:1010.4527 Traces in monoidal categories. Stephan Stolz , Peter Teichner math.CT math.AT Cross-listings 27 Oct arXiv:1010.5397 Mirror stability conditions and SYZ conjecture for Fermat polynomials. So Okada math.AG math.CT math.RT ... math.SG Revisions 29 Oct arXiv:1009.0234 Categorical Non-standard Analysis. Hayato Saigo math.CT 29 Oct arXiv:1004.0160 Stone duality for topological theories. Dirk Hofmann , Isar Stubbe math.CT

36. Homological Algebra File Format PDF/Adobe Acrobat Quick View http://www.maths.gla.ac.uk/~phk/kap1.pdf

37. Homological Algebra In NLab Idea. From a modern perspective, homological algebra is the study of algebraic objects, (such as groups, rings or Lie algebras, or sheaves of such objects), by ‘resolving http://ncatlab.org/nlab/show/homological algebra

nLab homological algebra Skip the Navigation Links Home Page All Pages Recently Revised ... Export Context Homological algebra homological algebra and nonabelian homological algebra Context additive and abelian categories additive category abelian category semi-abelian category Basic definitions kernel cokernel complex differential ... projective object Higher category notions derived category derived functor Tor Ext ... differential graded category Lemmas five lemma snake lemma Theorems Dold-Kan correspondence Moore complex Eilenberg-Zilber theorem cochain on a simplicial set ... Edit this sidebar Contents Idea Entries in homological algebra References Idea From a modern perspective, homological algebra is the study of algebraic objects, (such as groups, rings or Lie algebras, or sheaves of such objects), by ‘resolving them’, replacing them by more stable objects whose homotopy category is the derived category of an abelian category Functors between the original algebraic objects lead to derived functor s between the homotopy categories , and much effort is devoted to the study of those derived functors, and the interpretation of their properties in terms of structure of the original algebraic objects. There are variants of the above idea that handle more non-linear phenomena. These include non-Abelian (co)homology and crossed and quadratic versions that use a small degree of non-linearity in the models. These latter theories make extensive use of techniques from

38. HOMOLOGICAL ALGEBRA 5 4.7. Tensoringofnite abelian groups over Z 106 Homework 5 106 5.0. Inverse image and the direct image of Dmodules 106 5.1. Multiple tensor products. 107 5.2. http://www.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/1.Spr

39. 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 finite-dimensional 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 2010-2011 Representation Theory (Level M, 1st semester): Home page Group Theory (Level 3, 1st semester): Home page Algebraic Topology (Level M, 2nd semester): 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

40. MATH 602. Homological Algebra MATH 602. Homological Algebra (Spring 2007) Meeting times MWF, 900am950am (MTH 1311) Instructor Professor Jonathan Rosenberg. His office is room 2114 of the Math Building, phone http://www.math.umd.edu/users/jmr/602/

MATH 602. Homological Algebra (Spring 2007) Meeting times: MWF, 9:00am-9:50am (MTH 1311) Instructor: Professor Jonathan Rosenberg . His office is room 2114 of the Math Building, phone extension 55166, or you can contact him by email . His office hours are M and F 1-2, or by appointment. Text: . The text has a reasonable list price, $43. Errata for the text may be found here or here . Weibel also has an article about the history of homological algebra Prerequisite: MATH 600 (graduate algebra). MATH 734 (algebraic topology) or MATH 606 (algebraic geometry) helps in terms of motivation, but won't be assumed. Catalog description: Projective and injective modules, homological dimensions, derived functors, spectral sequence of a composite functor. Applications. Course Description: This course will introduce the basic methods of homological algebra, and discuss such topics as chain complexes and spectral sequences. This material is essential for algebraic geometry and algebraic topology , and plays a major role in many other subjects as well. We will do applications to subjects such as cohomology of groups and Hochschild cohomology of algebras. If we have time, we may get to some more "modern" topics such as derived and triangulated categories. But at a minimum, I hope you will come out of the course knowing how to compute with spectral sequences. In terms of Weibel's book, I hope at a minimum to cover chapters 1 (chain complexes), 2 (derived functors), 3 (Ext and Tor), 5 (spectral sequences), 6 (group homology and cohomology), and 9 (Hochschild and cyclic homology), plus the appendix on category theory (as this is quite important and is often not covered in other courses). If time permits we may cover parts of the other chapters also.

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