From Groups to Categorial Algebra: Introduction to Protomodular and Mal’tsev Categories - Brossura

Bourn, Dominique

Brossura

ISBN 10: 3319572180 ISBN 13: 9783319572185

Casa editrice: Birkhäuser, 2017

Riassunto

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. 

Su questo libro

Informazioni sull?autore

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

Dalla quarta di copertina

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. 

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3319572180
• ISBN 13: 9783319572185
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 120
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania