Getting Started With Category Theory: What You Need to Know

[Synchronised]

I am interested in learning category theory, just for extracurricular knowledge so I watched a 30 minute YouTube video but I had no idea what the guy was talking about :( what do I need to know before learning Cat. theory?

 

[Number Nine]

As far as formal prerequisites go? Not very much, though having a stock of examples certainly helps (topological spaces, metric spaces, group, rings, fields, etc). The material is abstract enough that I really wasn't comfortable with the idea of a category until I had a fair bit of algebra under my belt.

 

[micromass]

You're in high school right? In that case, category theory isn't something you need to worry about right now. In order to study category theory, you must have a large amount of mathematical maturity. That is: category theory aims to generalize the structures of groups, rings, topological spaces, etc. Of course, to appreciate category theory, you first need to know some things about these various structures.

If you want to do category theory, then I'd say that you need to be quite strong in abstract algebra first. Knowledge of topology and other disciplines won't hurt either.

A course on set theory might be necessary as well. You must be comfortable with the distinction between a set and a class. And of course you must be very comfortable with functions and commutative diagrams.

I don't really know why you are so interested in category theory. Category theory is a very useful language and it can make a lot of things much easier. But on the other hand, category theory on its own tend to be quite dull for most people.

That said, there are some books out there which teach a baby version of category theory to a public that does not yet have the experience for an actual course. This book comes to mind: https://www.amazon.com/dp/052171916X/?tag=pfamazon01-20

 

[Synchronised]

I think I don't have the time to cover all of this, it seems like a very involved topic so I will just learn it later in uni. For now I will just concentrate on perfecting my high school curriculum and learn mathematical proves from the velleman book that you suggested, that seems like the best thing to do at the moment to both do well in my high school exams and first year uni :)

 

[homeomorphic]

That said, there are some books out there which teach a baby version of category theory to a public that does not yet have the experience for an actual course. This book comes to mind: https://www.amazon.com/Conceptual-Mat...ywords=Lawvere&tag=pfamazon01-20

Perhaps, that book shouldn't just be viewed as a baby-version for the public.

Of course, it is boring for someone like me to read the definition of a category when I already know it, and so on. It would also help to have a wider stock of examples to take advantage of. In that sense, category theory is a pretty advanced topic because although it doesn't have serious prerequisites, it is more or less impotent and useless, unless you have plenty of good examples in mind for all the concepts. That being said, I think people should be cautious before declaring a book to be too easy for them. Easy is good. What makes things unsuitable is if you already know the stuff very well.

Baez said something about that book like at some point, if you don't do all the exercise, they will switch from being super easy to very difficult at some point in the book. He also said if you read the whole thing, you'll learn parts of topos theory almost subconsciously or something like that, if I remember right. This is from one of the masters of categories. In addition, it's a very well-written book, so there's something to be said for that. Better to have fun reading Conceptual Mathematics than falling asleep in the middle of MacLane's Categories for the Working Mathematican, unless sleep is your goal.