I am wondering how much set theory is needed to read the basics of category theory, and what (preferrably short) book would be recommended.
Usually I would just use naive set theory without worrying whether something is really a set, so it bugs me quite a lot that we have small/locally small/large category where we need to specify certain things to be a set. I have never worked with axiomatic set theory before, and I don't think I am interested in going into the foundation deeply: I just want to know enough about/be comfortable with classes etc to read category theory or homological algebra.
I wiki-ed a bit and there seems to be different axioms for set theory. As classes are involved, I guess I should be looking at NBG or MK axioms.
So can anyone briefly tell me how much knowledge in set theory would suffice, or whether there are short notes/books that would serve this purpose. Thanks!