Derived Functors In Relative Homological Algebra
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Derived Functors In Relative Homological Algebra
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Author : Franklin Stauffer Brenneman
language : en
Publisher:
Release Date : 1967
Derived Functors In Relative Homological Algebra written by Franklin Stauffer Brenneman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Foundations Of Relative Homological Algebra
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Author : Samuel Eilenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1965
Foundations Of Relative Homological Algebra written by Samuel Eilenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Algebra, Homological categories.
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.
Relative Homological Algebra
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Author : Edgar E. Enochs
language : en
Publisher: Walter de Gruyter
Release Date : 2011-10-27
Relative Homological Algebra written by Edgar E. Enochs and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-27 with Mathematics categories.
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.
The Derived Functors Of Im Relative Homological And Homotopical Algebra
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Author : J.-M. Cordier
language : en
Publisher:
Release Date : 1981
The Derived Functors Of Im Relative Homological And Homotopical Algebra written by J.-M. Cordier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Rational Representations The Steenrod Algebra And Functor Homology
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Author : Vincent Franjou
language : en
Publisher:
Release Date : 2003
Rational Representations The Steenrod Algebra And Functor Homology written by Vincent Franjou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and $K$-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights. T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashvili present A. Scorichenko's understanding of the stable $K$-theory of rings as functor homology. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Homological Algebra Pms 19 Volume 19
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Author : Henry Cartan
language : en
Publisher: Princeton University Press
Release Date : 2016-06-02
Homological Algebra Pms 19 Volume 19 written by Henry Cartan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.
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.
Homotopical Algebra
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Author : Daniel G. Quillen
language : en
Publisher: Springer
Release Date : 2006-11-14
Homotopical Algebra written by Daniel G. Quillen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Relative Derived Functors And The Homology Of Groups
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Author : G. J. Ellis
language : en
Publisher:
Release Date : 1987
Relative Derived Functors And The Homology Of Groups written by G. J. Ellis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Algebraic Topology A Structural Introduction
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-12-24
Algebraic Topology A Structural Introduction written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Mathematics categories.
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
Seminar On Triples And Categorical Homology Theory
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Author : H. Appelgate
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1969-02
Seminar On Triples And Categorical Homology Theory written by H. Appelgate and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969-02 with Mathematics categories.