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From Groups to Categorial Algebra : Introduction to Protomodular and Mal’tsev Categories / by Dominique Bourn.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Bourn, Dominique., Author.
- Series:
- Compact Textbooks in Mathematics, 2296-4568
- Language:
- English
- Subjects (All):
- Algebra.
- Categories (Mathematics).
- Algebra, Homological.
- General Algebraic Systems.
- Category Theory, Homological Algebra.
- Local Subjects:
- General Algebraic Systems.
- Category Theory, Homological Algebra.
- Physical Description:
- 1 online resource (XII, 106 p.)
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
- Summary:
- 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. .
- Contents:
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-319-57219-9
- OCLC:
- 1017902785
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