From Groups to Categorial Algebra

Introduction to Protomodular and Mal’tsev Categories

Nonfiction, Science & Nature, Mathematics, Algebra, History
Cover of the book From Groups to Categorial Algebra by Dominique Bourn, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Dominique Bourn ISBN: 9783319572192
Publisher: Springer International Publishing Publication: June 13, 2017
Imprint: Birkhäuser Language: English
Author: Dominique Bourn
ISBN: 9783319572192
Publisher: Springer International Publishing
Publication: June 13, 2017
Imprint: Birkhäuser
Language: English

This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via “universal properties”, a view on that group “from the outside”. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects.

By introducing  protomodular categories and Mal’tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups.

Hardly any previous knowledge of category theory is assumed, and just a little experience with standard algebraic structures such as groups and monoids.  Examples and exercises help understanding the basic definitions and results throughout the text. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via “universal properties”, a view on that group “from the outside”. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects.

By introducing  protomodular categories and Mal’tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups.

Hardly any previous knowledge of category theory is assumed, and just a little experience with standard algebraic structures such as groups and monoids.  Examples and exercises help understanding the basic definitions and results throughout the text. 

More books from Springer International Publishing

Cover of the book Cyber Security Cryptography and Machine Learning by Dominique Bourn
Cover of the book Programming Languages by Dominique Bourn
Cover of the book Formal Modeling and Analysis of Timed Systems by Dominique Bourn
Cover of the book Particle Panic! by Dominique Bourn
Cover of the book An Excursion through Elementary Mathematics, Volume II by Dominique Bourn
Cover of the book Recent Advances in Technology Research and Education by Dominique Bourn
Cover of the book Dynamics of Coupled Structures, Volume 1 by Dominique Bourn
Cover of the book Resilience by Design by Dominique Bourn
Cover of the book The Strange Persistence of Universal History in Political Thought by Dominique Bourn
Cover of the book Diagnostic and Therapeutic Neuroradiology by Dominique Bourn
Cover of the book Mathematical Morphology and Its Applications to Signal and Image Processing by Dominique Bourn
Cover of the book Scalar Wave Driven Energy Applications by Dominique Bourn
Cover of the book Nutrition Management of Inherited Metabolic Diseases by Dominique Bourn
Cover of the book Poverty Reduction, Education, and the Global Diffusion of Conditional Cash Transfers by Dominique Bourn
Cover of the book Agent-Mediated Electronic Commerce. Designing Trading Strategies and Mechanisms for Electronic Markets by Dominique Bourn
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy