From Groups to Categorial Algebra - pr_64553

From Groups to Categorial Algebra

Introduction to Protomodular and Mal'tsev Categories



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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.

Product code: 9783319572185

ISBN 9783319572185
Dimensions (HxWxD in mm) H235xW155
Series Compact Textbooks in Mathematics
No. Of Pages 106
Publisher Birkhauser Verlag AG
Edition 1st ed. 2017