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Mal'cev, Protomodular, Homological and Semi-Abelian Categories : Mathematics and Its Applications - Francis Borceux

Mal'cev, Protomodular, Homological and Semi-Abelian Categories

Mathematics and Its Applications

Hardcover Published: 29th February 2004
ISBN: 9781402019616
Number Of Pages: 480

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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.

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)

Metatheoremsp. 1
Intrinsic centralityp. 11
Mal'cev categoriesp. 125
Protomodular categoriesp. 229
Homological categoriesp. 273
Semi-abelian categoriesp. 319
Strongly protomodular categoriesp. 345
Essentially affine categoriesp. 371
Algebraic theoriesp. 399
Internal relationsp. 411
Internal groupoidsp. 417
Variations on epimorphismsp. 427
Regular and exact categoriesp. 436
Monadsp. 449
Fibrationsp. 461
Classification table of the fibration of pointsp. 466
Bibliographyp. 467
Index of symbolsp. 473
Index of definitionsp. 475
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781402019616
ISBN-10: 1402019610
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 480
Published: 29th February 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.98

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