From Groups to Categorial Algebra

Introduction to Protomodular and Mal’tsev Categories
1. Auflage 2017
ISBN: 978-3-319-57218-5
Verlag: Birkhäuser

Buch, Englisch, 106 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1942 g

Reihe: Compact Textbooks in Mathematics

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. 

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Bourn, Dominique

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Basic concepts in category theory.- Internal structures.- Four basic facts in Algebra.- Unital and protomodular categories.- Regular and homological categories.- Linear and additive categories.- Mal’tsev, naturally Mal’tsev categories.

Über Autor(innen)

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