Basic Category Theory: 143 (Cambridge Studies in Advanced Mathematics, Series Number 143)
Cambridge University Press, 7/24/2014
EAN 9781107044241, ISBN10: 1107044243
Hardcover, 190 pages, 23.1 x 15 x 1.5 cm
Language: English
Originally published in English
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.
Note to the reader
Introduction
1. Categories, functors and natural transformations
2. Adjoints
3. Interlude on sets
4. Representables
5. Limits
6. Adjoints, representables and limits
Appendix
proof of the General Adjoint Functor Theorem
Glossary of notation
Further reading
Index.