Download or read book Foundation of Relative Non abelian Homological Algebra written by Tamar Janelidze and published by . This book was released on 2009 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Relative Homological Algebra written by Samuel Eilenberg and published by American Mathematical Soc.. This book was released on 1965 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main notion of this paper is that of a "projective class of sequences" in an arbitrary (pointed) category. Each such class carries with it its own projective objects. One can then talk about projective resolutions, and if the category is additive, all the usual properties of the resolutions hold. In particular, this will permit the development of homological algebra in some additive categories which are not abelian, e.g., the category of comodules over a coalgebra over an arbitrary commutative ring.
Download or read book Non Abelian Homological Algebra and Its Applications written by Hvedri Inassaridze and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes methods of non-abelian homological algebra, such as the theory of satellites in abstract categories with respect to presheaves of categories and the theory of non-abelian derived functors of group valued functors. Applications to K-theory, bivariant K-theory and non-abelian homology of groups are given. The cohomology of algebraic theories and monoids are also investigated. The work is based on the recent work of the researchers at the A. Razmadze Mathematical Institute in Tbilisi, Georgia. Audience: This volume will be of interest to graduate students and researchers whose work involves category theory, homological algebra, algebraic K-theory, associative rings and algebras; algebraic topology, and algebraic geometry.
Download or read book Homological Algebra written by Marco Grandis and published by World Scientific. This book was released on 2013 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a study of semi-exact homological categories as a basis for a generalized homological algebra. The aim is to extend homological notions to deeply non-abelian situations, where satellites and spectral sequences produced by unstable homotopy can still be studied.
Download or read book Foundations of Relative Homological Algebra written by Samuel Eilenberg and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Relative Homological Algebra written by Samuel Eilenberg and published by . This book was released on with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relative Homological Algebra written by Edgar E. Enochs and published by Walter de Gruyter. This book was released on 2011-10-27 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.
Download or read book Homological Algebra written by Marco Grandis and published by World Scientific. This book was released on 2012 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations. These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system. The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a 'Coherence Theorem for homological algebra'. (On the contrary, a 'non-distributive' homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.) The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences. We thus establish an effective method of working with spectral sequences, called 'crossword chasing', that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.
Download or read book Homological Algebra written by Henri Cartan and published by Princeton University Press. This book was released on 1999-12-19 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Relative Homological Algebra written by Edgar E. Enochs and published by Walter de Gruyter. This book was released on 2011-08-29 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume deals with the relative homological algebra of complexes of modules and their applications. It is a concrete and easy introduction to the kind of homological algebra which has been developed in the last 50 years. The book serves as a bridge between the traditional texts on homological algebra and more advanced topics such as triangulated and derived categories or model category structures. It addresses to readers who have had a course in classical homological algebra, as well as to researchers.
Download or read book An Introduction to Homological Algebra written by Joseph J. Rotman and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman’s book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two.
Download or read book An Elementary Approach to Homological Algebra written by L.R. Vermani and published by CRC Press. This book was released on 2003-05-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. However, few, if any, of these books are written at a level appropriate for students approaching the subject for the first time. An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning
Download or read book Homological Algebra In Strongly Non abelian Settings written by Marco Grandis and published by World Scientific. This book was released on 2013-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on ‘Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups’, published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell — a moderate generalisation of abelian categories that is nevertheless crucial for a theory of ‘coherence’ and ‘universal models’ of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.According to the present definitions, a semiexact category is a category equipped with an ideal of ‘null’ morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include their codomains, since the sequences of homotopy ‘objects’ for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.
Download or read book On the concept of non abelian category and Fr lich s non abelian homological algebra written by Paul Dedecker and published by . This book was released on 1964 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homological Algebra written by S.I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1994 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: A portrait of the subject of homological algebra as it exists today.
Download or read book Abelian Groups Rings Modules and Homological Algebra written by Pat Goeters and published by CRC Press. This book was released on 2016-04-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
