Overview
- Entirely self-contained non-technical introduction to protomodular categories—and 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
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents (7 chapters)
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About this book
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.
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Bibliographic Information
Book Title: From Groups to Categorial Algebra
Book Subtitle: Introduction to Protomodular and Mal’tsev Categories
Authors: Dominique Bourn
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-319-57219-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-57218-5Published: 26 June 2017
eBook ISBN: 978-3-319-57219-2Published: 13 June 2017
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XII, 106
Topics: General Algebraic Systems, Category Theory, Homological Algebra