From Groups to Categorial Algebra

Introduction to Protomodular and Mal’tsev Categories

  • Dominique Bourn

Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Dominique Bourn
    Pages 1-25
  3. Dominique Bourn
    Pages 27-32
  4. Dominique Bourn
    Pages 33-41
  5. Dominique Bourn
    Pages 43-57
  6. Dominique Bourn
    Pages 59-69
  7. Dominique Bourn
    Pages 71-77
  8. Dominique Bourn
    Pages 79-100
  9. Back Matter
    Pages 101-106

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. 


group category of groups pullback in a category internal group in a category protomodular mal'tsev

Authors and affiliations

  • Dominique Bourn
    • 1
  1. 1.Departmente de MathematiquesUniversite du Littoral Departmente de MathematiquesCalaisFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-57218-5
  • Online ISBN 978-3-319-57219-2
  • Series Print ISSN 2296-4568
  • Series Online ISSN 2296-455X
  • Buy this book on publisher's site