- Author:
- Harold Simmons
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.
Cited By
- Saigo H, Naruse M, Okamura K, Hori H, Ojima I and Selişteanu D (2019). Analysis of Soft Robotics Based on the Concept of Category of Mobility, Complexity, 2019, Online publication date: 1-Jan-2019.
- Chiaselotti G, Ciucci D, Gentile T and Infusino F (2016). The granular partition lattice of an information table, Information Sciences: an International Journal, 373:C, (57-78), Online publication date: 10-Dec-2016.
Index Terms
- An Introduction to Category Theory
Recommendations
Jacques Carette
Category theory, as a discipline in mathematics, is now quite old. However, it took a fair amount of time for the subject to gain a solid foothold in mathematics. Even more recent (outside of a few trailblazers in the '70s and '80s) is the widening application of category theory to various areas in computing. Programming language semantics and theoretical software engineering now routinely use categorical language. So every new introduction to category theory is potentially welcome, as it may help educate a new generation of computer scientists on this fairly abstract but oh-so-useful topic. Simmons' introduction to the topic is a pedagogical marvel. It could just as easily have been titled A first category theory workbook , as its pedagogical style is to teach the reader who is willing to actually do (some of) the plentiful exercises in the book. This is really not a book one just reads. This is more like a guide for the serious student. This means, for example, that this book would make a terrible reference manual for category theory. But that is part of its success (pedagogically speaking). It does what it aims to do extremely well and does not pretend to be anything else. The writing is crisp and engaging. The author speaks directly to the reader, and the text is infused with subtle humor throughout (unfortunately, it appears as though the editor asked for some jokes to be removed; I would have preferred otherwise). The material is presented in a modern manner. In other words, it reflects our best current understanding of categories as simultaneously generalizing presets and monoids. It also uses a clever split-page layout for a lot of statements that accurately reflect the dualities omnipresent in the material. Furthermore, it specifically aims to build up intuition about the topic, without offering misleading analogies. From a computing perspective, the only downside of this book is that it is squarely aimed at students of mathematics. The mathematics is not difficult, but some examples relevant to computing would make it more approachable to students of computing or software engineering. It would be intriguing to see an alternate edition with the same engaging style, but with exercises and examples drawn from computing. I give this book my highest possible recommendation. I will use it as a textbook in a course in category theory (for computing), and I will follow its pedagogical style, although I will supplement the exercises with more computing content. I am aware of various introductions to category theory aimed at computer scientists and/or software engineers, but none can quite match this one for pedagogical brilliance. Online Computing Reviews Service
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