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Mal`cev, Protomodular, Homological and Semi-Abelian Categories, Borceux Francis, Bourn Dominique



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Автор: Borceux Francis, Bourn Dominique
Название:  Mal`cev, Protomodular, Homological and Semi-Abelian Categories
ISBN: 9781402019616
Издательство: Springer
Классификация:
ISBN-10: 1402019610
Обложка/Формат: Hardback
Страницы: 479
Вес: 1.92 кг.
Дата издания: 2004
Серия: Mathematics and Its Applications
Язык: English
Иллюстрации: 1, black & white illustrations
Размер: 25.20 x 16.15 x 2.64
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Дополнительное описание: Формат: 240x160
Круг читателей: Researchers in category theory, homology theory and universal algebra
Ключевые слова:
Язык: eng
Оглавление: PrefaceMetatheorems0.1 The Yoneda embedding 0.2 Pointed categories 1 Intrinsic centrality 1.1 Spans and relations1.2 Unital categories 1.3 Cooperating and central morphisms 1.4 Commutative objects 1.5 Symmetrizable morphisrns 1.6 Regular unital categories 1.7 Associated abelian object 1.8 Strongly unital categories 1.9 Gregarious objects 1.10 Linear and additive categories 1.11 Antilinear and antiadditive categories 1.12 Complemented subobjects 2 Mal’cev categories 2.1 Slices, coslices and points 2.2 Mal’cev categories 2.3 Abelian objects in Mal’cev categories 2.4 Naturally Mal’cev categories 2.5 Regular Mal’cev categories 2.6 Connectors in Mal’cev categories 2.7 Connector and cooperator 2.8 Associated abelian object and commutator 2.9 Protoarithmetical categories 2.10 Antilinear Mal’cev categories 2.11 Abelian groupoids 3 Protomodular categories 3.1 Definition and examples 3.2 Normal subobjects 3.3 Couniversal property of the product 3.4 Groupoids, protomodularity and normality 4 Homological categories 4.1 The short five lemma 4.2 The nine lemma 4.3 The Noether isomorphism theorems 4.4 The snake lemma 4.5 The long exact homology sequence 4.6 Examples of homological categories 5 Semi-abelian categories 5.1 Definition and examples 5.2 Semi-direct products 5.3 Semi-associative Mal’cev varieties 6 Strongly protomodular categories 6.1 Centrality and normality 6.2 Normal subobjects in the fibres 6.3 Normal functors 6.4 Strongly protomodular categories 6.5 A counterexample 6.6 Connector and cooperator 7 Essentially affine categories 7.1 The fibration of points 7.2 Essentially affine categories 7.3 Abelian extensions Appendix A.1 Algebraic theories A.2 Internal relations A.3 Internal groupoids A.4 Variations on epimorphisms A.5 Regular and exact categories A.6 Monads A.7 Fibrations Classification table of the fibration of points Bibliography Index of symbols Index of definitions





Categories for the Working Mathematician

Автор: Mac Lane
Название: Categories for the Working Mathematician
ISBN: 0387984038 ISBN-13(EAN): 9780387984032
Издательство: Springer
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Цена: 8309 р.
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Описание: Describes the concepts of category, functor, natural transformation, and duality. This book focuses on adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits.

Triangulated Categories

Автор: Holm
Название: Triangulated Categories
ISBN: 0521744318 ISBN-13(EAN): 9780521744317
Издательство: Cambridge Academ
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Цена: 11568 р.
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Описание: Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. These self-contained articles are a useful introduction for graduate students entering the field and a valuable reference for experts.

Module Categories of Analytic Groups

Автор: Magid
Название: Module Categories of Analytic Groups
ISBN: 052109027X ISBN-13(EAN): 9780521090278
Издательство: Cambridge Academ
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Цена: 4518 р.
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Описание: Professor Magid has written a complete account of the subject that is accessible to a wide audience.

Categories and Modules with K-Theory in View

Автор: Berrick
Название: Categories and Modules with K-Theory in View
ISBN: 0521632765 ISBN-13(EAN): 9780521632768
Издательство: Cambridge Academ
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Цена: 18620 р.
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Описание: This is a concise introduction at graduate level to ring theory, module theory and number theory.

Frobenius Categories versus Brauer Blocks

Автор: Lluis Puig
Название: Frobenius Categories versus Brauer Blocks
ISBN: 376439997X ISBN-13(EAN): 9783764399979
Издательство: Springer
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Цена: 17819 р.
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Описание: Introduces and develops the abstract setting of the Frobenius categories for an understanding of what was loosely called the local theory either of finite groups or of blocks, and for the purpose of an eventual classification.

Introduction to Categories, Homological Algebra and Sheaf Cohomology

Автор: Strooker
Название: Introduction to Categories, Homological Algebra and Sheaf Cohomology
ISBN: 0521095255 ISBN-13(EAN): 9780521095259
Издательство: Cambridge Academ
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Цена: 6868 р.
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Описание: Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields.

Homological Algebra of Semimodules and Semicontramodules

Автор: Positselski
Название: Homological Algebra of Semimodules and Semicontramodules
ISBN: 3034604351 ISBN-13(EAN): 9783034604352
Издательство: Springer
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Цена: 16334 р.
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Описание: 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.

Methods of Homological Algebra

Автор: Gelfand Sergei I., Manin Yuri I.
Название: Methods of Homological Algebra
ISBN: 3540435832 ISBN-13(EAN): 9783540435839
Издательство: Springer
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Цена: 14849 р.
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Описание: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

Introduction to Homological Algebra, 85,

Автор: Joseph J. Rotman
Название: Introduction to Homological Algebra, 85,
ISBN: 0125992505 ISBN-13(EAN): 9780125992503
Издательство: Elsevier Science
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Цена: 8160 р.
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Описание: An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author's attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.

An Introduction to Homological Algebra

Автор: Northcott
Название: An Introduction to Homological Algebra
ISBN: 0521097932 ISBN-13(EAN): 9780521097932
Издательство: Cambridge Academ
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Цена: 7410 р.
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Описание: This book is designed with the needs and problems of the beginner in mind, but will also be a useful work of reference for specialists.

Toroidal Groups / Line Bundles, Cohomology and Quasi-Abelian Varieties

Автор: Abe Yukitaka, Kopfermann Klaus
Название: Toroidal Groups / Line Bundles, Cohomology and Quasi-Abelian Varieties
ISBN: 3540419896 ISBN-13(EAN): 9783540419891
Издательство: Springer
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Цена: 4448 р.
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Описание: Toroidal groups are the connecting link between torus groups and any complex Lie groups. Many properties of complex Lie groups such as the pseudoconvexity and cohomology are determined by their maximal toroidal subgroups. Quasi-Abelian varieties are meromorphically separable toroidal groups. They are the natural generalisation of the Abelian varieties. Nevertheless, their behavior can be completely different as the wild groups show.

Complex Abelian Varieties

Автор: Birkenhake Christina, Lange Herbert
Название: Complex Abelian Varieties
ISBN: 3540204881 ISBN-13(EAN): 9783540204886
Издательство: Springer
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Цена: 17819 р.
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Описание: The subject of this book is the theory of abelian varieties over the field of complex numbers. It covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results on Jacobians and Prym varieties allow applications to the theory of algebraic curves. The second edition contains five new chapters which present some of the most important recent result on the subject. Among them are results on automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture.


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