An Introduction to Category Theory

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Cambridge University Press, Sep 22, 2011 - Mathematics
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Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.
 

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Contents

1 Categories
1
2 Basic gadgetry
34
3 Functors and natural transformations
72
4 Limits and colimits in general
108
5 Adjunctions
148
6 Posets and monoid sets
190
Bibliography
223
Index
224
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About the author (2011)

Harold Simmons is officially retired but still active in research. He also teaches postgraduate courses in the School of Mathematics at the University of Manchester.

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