From Groups to Categorial Algebra : Introduction to Protomodular and Mal'tsev Categories

Dominique Bourn

ISBN 10: 3319572180 / ISBN 13: 9783319572185

Editore: Springer, Berlin, Birkhäuser, 2017

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Druck auf Anfrage Neuware - Printed after ordering - This book gives a thorough and entirely self-contained, in-depth introduction to a specificapproach to group theory, in a large sense of that word. Thefocus lieon 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 groupsalone, but applies equally well to other similar categories of algebraic objects.By introducingprotomodular categories and Mal'tsev categories, which form a larger class, thestructural properties of the category Gp of groups, showhow they emerge from four very basic observations about the algebraic litteral calculus andhow, 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 littleexperience with standard algebraic structures such as groups and monoids. Examples and exercises help understanding the basicdefinitions and results throughout the text.

Codice articolo 9783319572185

Dati bibliografici

• Titolo: From Groups to Categorial Algebra : Introduction to Protomodular and Mal'tsev Categories
• Editore: Springer, Berlin, Birkhäuser
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3319572180
• ISBN 13: 9783319572185
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 236 L x 145 A x 8 P (millimetri) 236 millimetri di larghezza per 145 millimetri di altezza per 8 millimetri di profondità
• Peso: 195 grammi

Descrizione articolo

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. 

Informazioni sull'autore

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