An Invitation to General Algebra and Universal Constructions
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edition: | 2nd ed. 2015. |
| Series: | Universitext,
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| Online Access: | https://doi.org/10.1007/978-3-319-11478-1 |
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Table of Contents:
- 1 About the course, and these notes
- Part I: Motivation and Examples
- 2 Making Some Things Precise
- 3 Free Groups
- 4 A Cook's Tour
- Part II: Basic Tools and Concepts
- 5 Ordered Sets, Induction, and the Axiom of Choice
- 6 Lattices, Closure Operators, and Galois Connections
- 7 Categories and Functors
- 8 Universal Constructions
- 9 Varieties of Algebras
- Part III: More on Adjunctions
- 10 Algebras, Coalgebras, and Adjunctions
- References
- List of Exercises
- Symbol Index
- Word and Phrase Index.