From Groups to Categorial Algebra

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.

Entirely self-contained non-technical introduction to protomodular categoriesand to Mal'tsev categories Hardly any previous knowledge is assumed Examples and exercises isllustrate basic definitions and results Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras

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

Inhalt
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.