>>9830824A set is just some elements with some axioms, and you can build on it by defining functions and shit, a category can be passed on set theory, in that case a category is a set of things that satisfy some other axioms, but you don't actualy need sets, it can be classes, or even objects of other categories, a lot of times you just talk of some collection of things without even defining them.
The important point is that the axioms you have for a category are still loose enough so that you can build almost anything on it, just like set theory, but it's also constrained enough so that you can make some very cool theorems that work in any category, or large collections of categories, which abstract a lot of useful things from other areas of math.
If we do category theory over sets then a category is a set A of things we call arrows with the extra rules that
>There exists another set A3 of triplets of these arrows and we call the 3rd element the composition of the first and second one in the triplet>For each arrow a in A there are two elements r,l, such that (l,a,a) in A3 and (a,r,a) in A3>If r,l, are present in multiple triplets they will always be in triplets if the above formI thinks thats all, I'm a bit rusty.
