[adamnemecek]

You might be interested in "Algebra: Chapter 0" http://amzn.to/2iYpAn5

"The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics."

[Koshkin]

> categories, used as a unifying theme in the presentation of the main topics

Categories are not a good way to be introduced to the "main topics" of abstract algebra. Yes, Category Theory can be seen as the "Chapter 0" of a course on abstract algebra, but for beginners a traditional presentation based on sets would be much easier to digest.

There is a similarity between using categories and using functional programming style or a language - as opposed to using an approach to mathematics based on sets and using the imperative programming style or a language: the latter is just more intuitive and therefore easier to learn for a beginner.

[j2kun]

> for beginners a traditional presentation based on sets would be much easier to digest.

If you read the referenced book, you'd know the author does exactly this.

[maxiepoo]

Do you have experience teaching both or are you just speculating?

[keyboardwriter]

Thanks, but is this another textbook that requires knowledge in abstract algebra prior to reading it, or make any sort of previous knowledge assumptions?

[qwerty12653]

Having attempted to get through it myself(and having a math degree), I would strongly recommend against Algebra: Chapter 0 as an introductory text on either category theory or abstract algebra.

If you either already have a math degree, or if you're already at the point where you're ready to take an upper-level undergraduate math course, then it may be a decent book for you. Maybe. For example, if you're:

- already very comfortable with linear algebra

- possibly been exposed to a bit of topology in analysis class

- already been exposed to abstract algebra a bit by a more theoretical approach to linear algebra (comfortable with proving things in linear algebra via vector spaces and fields)

Otherwise, I would absolutely steer clear of it. The writing style is also not terribly beginner-friendly, in my opinion.

The closest book I can think of to what you're asking for would be "Conceptual Mathematics: A First Introduction to Categories". Though obviously I don't know whether it's a good fit for your particular background and learning style.

[j2kun]

I think the first chapter definitely has no prerequisites (it introduces sets and categories), but it's also a core mathematics textbook intended for upper-level undergraduate and early graduate students in pure mathematics. So it re-teaches all of abstract algebra, and quite a bit beyond, using category theory as a unifying principle. It's a book intended to give you a mature perspective and prime you for research.

[GFK_of_xmaspast]

Not sure I see the point in trying to learn category theory without algebra to motivate it.

[adamnemecek]

You might be interested in this then https://news.ycombinator.com/item?id=13268335

The book doesn't really require much knowledge.

[keyboardwriter]

I'll check out this book then. Has great reviews.