Relative Homological Algebra And Exact Model Structures
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Relative Homological Algebra And Exact Model Structures
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Author :
language : en
Publisher:
Release Date : 2019
Relative Homological Algebra And Exact Model Structures written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Relative Homological Algebra
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Author : Edgar E. Enochs
language : en
Publisher: Walter de Gruyter
Release Date : 2011-08-29
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 2011-08-29 with Mathematics categories.
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.
Introduction To Abelian Model Structures And Gorenstein Homological Dimensions
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Author : Marco A. P. Bullones
language : en
Publisher: CRC Press
Release Date : 2016-08-19
Introduction To Abelian Model Structures And Gorenstein Homological Dimensions written by Marco A. P. Bullones and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey’s work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this book presents new results in relative homological algebra and model category theory. The author also re-proves some established results using different arguments or from a pedagogical point of view. In addition, he proves folklore results that are difficult to locate in the literature.
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.
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.
Homological Algebra
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2012
Homological Algebra 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 2012 with Mathematics categories.
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.
Homological Algebra Of Semimodules And Semicontramodules
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Author : Leonid Positselski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Homological Algebra Of Semimodules And Semicontramodules written by Leonid Positselski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.
This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.
Homological Algebra
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2013
Homological Algebra 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 2013 with Mathematics categories.
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.
Homotopical And Homological Algebra Of Exact Couples
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Author : Jonathan Peter Rogness
language : en
Publisher:
Release Date : 2005
Homotopical And Homological Algebra Of Exact Couples written by Jonathan Peter Rogness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.