Grandis Marco Homological Algebra: In Strongly Non-Abelian Settings 9789814425919

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Автор: Grandis Marco
Название: Homological Algebra: In Strongly Non-Abelian Settings
ISBN: 9789814425919
Издательство: World Scientific Publishing
Классификация:

Алгебра

Геометрия

Топология

Комбинаторика и теория графов

ISBN-10: 9814425915
Обложка/Формат: Hardback
Страницы: 356
Вес: 0.64 кг.
Дата издания: 06.03.2013
Серия: Mathematics
Язык: English
Иллюстрации: Black & white illustrations
Размер: 231 x 152 x 25
Читательская аудитория: Postgraduate, research & scholarly
Ключевые слова: Algebra, MATHEMATICS / Algebra / General,MATHEMATICS / Geometry / Algebraic,MATHEMATICS / Number Theory
Основная тема: Mathematics / Commutative Algebra
Подзаголовок: In strongly non-abelian settings
Ссылка на Издательство: Link
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Поставляется из: Англии
Описание: We propose here a study of semiexact and homological categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups, published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell -- a moderate generalisation of abelian categories that is nevertheless crucial for a theory of coherence and universal models of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.According to the present definitions, a semiexact category is a category equipped with an ideal of null morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of pairs of topological spaces or groups; they also include their codomains, since the sequences of homotopy objects for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.

Homological Algebra: In Strongly Non-Abelian Settings, Grandis Marco