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Relative Derived Functors And The Homology Of Groups


Relative Derived Functors And The Homology Of Groups
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Relative Derived Functors And The Homology Of Groups


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.




Derived Functors And Sheaf Cohomology


Derived Functors And Sheaf Cohomology
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Author : Ugo Bruzzo
language : en
Publisher: World Scientific
Release Date : 2020-03-10

Derived Functors And Sheaf Cohomology written by Ugo Bruzzo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.


The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.



More About The Co Homology Of Groups And Associative Algebras


More About The Co Homology Of Groups And Associative Algebras
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Author : Hvedri Inassaridze
language : en
Publisher:
Release Date : 2018

More About The Co Homology Of Groups And Associative Algebras written by Hvedri Inassaridze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.


It is proved that the homology and cohomology theories of groups and associative algebras are non-abelian derived functors of the cokernel and kernel groups of higher dimensions of their defining standard chain and cochain complexes respectively. The same results are also obtained for the relative (co)homology of groups, the mod cohomology of groups and the cohomology of groups with operators. This allowed us to give an alternative approach to higher Hopf formulas for integral homology of groups. An axiomatic characterization of the relative cohomology of groups is given and higher relative ( + 1)-th cohomology of groups is described in terms of -fold extensions.



Lectures On Functor Homology


Lectures On Functor Homology
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Author : Vincent Franjou
language : en
Publisher: Birkhäuser
Release Date : 2015-12-08

Lectures On Functor Homology written by Vincent Franjou and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.


This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov’s lectures highlight topological invariants: homoto py and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé’s introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.



Group Derived Functors And Relative Representability


Group Derived Functors And Relative Representability
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Author : John Lauchlin MacDonald
language : en
Publisher:
Release Date : 1965

Group Derived Functors And Relative Representability written by John Lauchlin MacDonald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Group theory categories.




Functor Categories And Their Application To Relative Homology


Functor Categories And Their Application To Relative Homology
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Author : Peter J. Freyd
language : en
Publisher:
Release Date : 1962

Functor Categories And Their Application To Relative Homology written by Peter J. Freyd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Abelian categories categories.




Derived Functors In Relative Homological Algebra


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


Foundations Of Relative Homological Algebra
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Author : Samuel Eilenberg
language : en
Publisher:
Release Date : 1965

Foundations Of Relative Homological Algebra written by Samuel Eilenberg and has been published by 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.



Seminar On Triples And Categorical Homology Theory


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.




Derived Functors And B Cohomology On Quantum Groups


Derived Functors And B Cohomology On Quantum Groups
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Author : Marie Engelbrecht Hougaard
language : en
Publisher:
Release Date : 2009

Derived Functors And B Cohomology On Quantum Groups written by Marie Engelbrecht Hougaard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.