Borceux Francis, Bourn Dominique Mal`cev, Protomodular, Homological and Semi-Abelian Categories 9781402019616

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Автор: Borceux Francis, Bourn Dominique
Название: Mal`cev, Protomodular, Homological and Semi-Abelian Categories
Издательство: Springer
Классификация:
Математические основы
Алгебра
ISBN: 1402019610
ISBN-13(EAN): 9781402019616
ISBN: 1-402-01961-0
ISBN-13(EAN): 978-1-402-01961-6
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
Описание: The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Malcev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.
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 MalвЂ™cev categories 2.1 Slices, coslices and points 2.2 MalвЂ™cev categories 2.3 Abelian objects in MalвЂ™cev categories 2.4 Naturally MalвЂ™cev categories 2.5 Regular MalвЂ™cev categories 2.6 Connectors in MalвЂ™cev categories 2.7 Connector and cooperator 2.8 Associated abelian object and commutator 2.9 Protoarithmetical categories 2.10 Antilinear MalвЂ™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 MalвЂ™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

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