From Groups to Categorial Algebra: Introduction to Protomodular and Mal’tsev Categories (Compact Textbooks in Mathematics) - Softcover

Bourn, Dominique

Softcover

ISBN 10: 3319572180 ISBN 13: 9783319572185

Publisher: Birkhäuser, 2017

Synopsis

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. 

About this title

About the Author

Dominique Bourn is Professor at the Université du Littoral in Calais, France.

From the Back Cover

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. 

Edition details

• Publisher: Birkhäuser
• Publication date: 2017
• Language: English
• ISBN 10: 3319572180
• ISBN 13: 9783319572185
• Binding: Paperback
• Edition number: 1
• Number of pages: 118