An Introduction to Category Theory

Simmons, Harold
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.

'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.A crystal clear introduction to category theory that demystifies functors, natural transformations, limits and colimits, adjunctions and more. Any beginning postgraduate mathematician will find all they need in this excellent text to access the subject. Over 200 exercises are provided with solutions available online.

The basics of category theory beautifully explained with a wealth of exercises. Solutions are available online.

Preface; 1. Categories; 2. Basic gadgetry; 3. Functors and natural transformations; 4. Limits and colimits in general; 5. Adjunctions; 6. Posets and monoid sets; Bibliography; Index.