Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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 Mal'cev, 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.
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.
Similar content being viewed by others
Table of contents (8 chapters)
Reviews
From the reviews:
"This monograph gives, from a categorical point of view, a coherent unified presentation of several aspects of universal algebra. … This is done in an elegant, unifying way via introducing several new concepts concerning objects, morphisms, and categories. … It contains up-to-date results and it is mainly addressed to working researchers in the field … . The exposition is well organized and the presentation is smooth. … In conclusion the monograph fills a gap in the literature and certainly it will be a standard reference in the future." (Apostolos D. Beligiannis, Mathematical Reviews, 2005e)
"The aim of the book under review is to set out the material that has been developed around the concept of protomodularity … . The authors take a ‘step by step’ approach … . As a result, the book is … beneficial for students using the book as a textbook. And it should make a first rate textbook: the authors’ choice of materials is judicious … and the style of the book is clear and easy to follow." (Peter T. Johnstone, Zentralblatt MATH, Vol. 1061 (12), 2005)
Authors and Affiliations
Accessibility Information
PDF accessibility summary
This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format.
Bibliographic Information
Book Title: Mal'cev, Protomodular, Homological and Semi-Abelian Categories
Authors: Francis Borceux, Dominique Bourn
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-1-4020-1962-3
Publisher: Springer Dordrecht
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media B.V. 2004
Hardcover ISBN: 978-1-4020-1961-6Published: 29 February 2004
Softcover ISBN: 978-90-481-6551-3Published: 15 December 2010
eBook ISBN: 978-1-4020-1962-3Published: 12 June 2019
Edition Number: 1
Number of Pages: XIV, 480
Topics: Category Theory, Homological Algebra, Group Theory and Generalizations, Associative Rings and Algebras, Order, Lattices, Ordered Algebraic Structures, Topological Groups, Lie Groups