An invitation to general algebra and universal constructions.
The aim of this book is to survey the basic notions and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. The titles of the chapters are as follows: 1. About the Course and These Notes, 2. Motivation and Examples, 3. Free Groups, 4. A Cook's Tour of Other Universal Constructions, 5. Ordered Sets, Induction, and the Axiom of Choice, 6. Lattices, Closure Operators, and Galois Connections, 7. Categories and Functors, 8. Universal Constructions in Category-Theoretic Terms, 9. Varieties of Algebras, 9. Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints. The author goes along with a reader, shows a motivation and a lot of examples and exercises, leads him to get a common view over several branches of algebra and other disciplines, investigating well-known and some less known constructions. The fundamental part of the book is contained in Chapters 7-10, where a category-theoretic approach is applied. The author takes care in writing full proofs throughout the book and he shows also ways of possible applications. The text contains a wealth material and should serve as a textbook for readers interested in this field. For a review of the first ed. [Berkeley, CA: Henry Helson (1998)] see Zbl 0917.00001.
scientific article; zbMATH DE number 6350970