I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts about groups and modular arithmetic. Is it too early to start learning category theory? should I wait to take a course on abstract algebra?
Is it very important to use category theory facts in a first course in group theory, ring theory, fields and Galois theory, modules and tensor products (each of those is a one semester course), would that make it a 'better' course?
I was unsure to learn category theory early but this post Mathematical subjects you wish you learned earlier inspired me to ask you given my background.
Best Answer
Luckily these days there is a beautiful text that teaches algebra and category theory at the same time: Aluffi - Chapter 0. It deserves to be more well-known. Besides the fact that it uses (basic) category language from the outset, it is very well-written. If I would ever teach an algebra course, this would probably the text I would use.