An Introduction to Category Theory 1st Edition by Harold Simmons (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’ve tried several times to get a little bit better grasp on Category Theory and never got very far. The definition of a Category is not difficult, but, for the way my mind works, abstractionitis quickly sets in, causing acute mental paralysis. In so many other treatments I have tried to read, there is too much of a rush to talk about functors (which relate one category to another) without giving enough preliminary attention just to aspects of a category in se. One of the great strengths of this excellent presentation is that the author gives a couple of very simple and concrete categories to keep in the back of one’s mind, and this helps a lot with the later developments. The chapters are short, a great plus. I also enjoy very much the author’s sense of humor. I would certainly recommend this book as an introduction over any other I have seen.

⭐Some reviews indicate this book is an “easy” introduction to category theory (CT)–and it is well written–but that’s not its primary virtue. It is something even better: Simmons has the knack for writing concretely about an inherently abstract topic. One aspect of this talent is that he focuses on CT as a problem-solving tool. I’ve extensively explored the CT literature, and chapter four of this book provides one of the most cogent descriptions that I have seen of how to use CT as an analytic technique. The book also has one of the better accounts of how CT’s many ‘gadgets’ work together. Simmons provides an extensive number of exercises, with solutions available online. Any reader who works through them will be well prepared for the more abstract CT exemplars that dominate the field.

⭐After reading the first two chapters I googled the guy in hope of finding some other books he wrote. This is (introductory) category theory and category theory is, among other things, a peculiar way of thinking. This means that even when it’s easy it can be deeply disturbing. What I like about the Simmons book the most is that it is really well written and, at times, very funny.

⭐Maybe this book is good for one who already knows Category Theory but not for a person who tries to learn it from scratch. I had to go over all wikipedia for explanations… Even though those missed terms were closely related to Category theory, not that I don’t know math at all. I’m quite technical guy.

⭐This review specifically applies only to the Kindle edition of what my knowledgable friends tell me is a fine book in paper editions.Do not under any circumstances purchase the Kindle edition of this book, as I did.The diagrams are tiny and do not enlarge with the font. They are so faint that even a magnifying glass doesn’t let you read them.In another kind of book, this would be only annoying. But in a real sense, category theory IS the diagrams.

⭐Excellent introduction to the theory. Some of the terms the author uses are unfamiliar to me but maybe that’s my fault.

⭐Very basic, nice and slow intro but need to take your time with it, if you are not a professional mathematician.

⭐I just bought the Kindle edition, and I can read the diagrams perfectly on my iPad. I am not sure why someone gave a one star review because she could not read the Kindle edition diagrams.I bought this book because I wanted to hopefully improve my facility with the Haskell programming language. So far, this book satisfies that need.

⭐An excellent introduction for anyone with background from a first course in Abstract Algebra (groups, rings, fields) and basic familiarity with mathematical proofs as expected of a sophomore level mathematics major. An astute freshman may be able to grasp these concepts if his/her interests include such abstract concepts as those in Category Theory. This is the most ‘gentle’ introduction to the field that I have read. The next step from Simmons’ text would be the book by Steve Awodey. And if one wishes to go the expert route with Categories, proceed from these two, straight to Maclane’s Categories for the Working Mathematician.

⭐This is perhaps the most gentle introduction to category theory text around: suitable for a third or fourth year undergraduate. My only gripe is that the section on adjunctions is a bit confusing, and done in a “piecewise” manner that leaves the reader guessing as to what is going on until the end. Otherwise, the textbook is very clear and features plenty of helpful examples.

⭐I was looking for a practical introduction to category theory. This book is easy to read, explain good all contents but I was expecting a practical view (more practical examples). But not. Detailed definitions, but just definitions.

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