I don't think anyone's really answered my question but you've hit the closest to it I think, so I'll rephrase it in the hopes that you can clarify it for me: wh

I don't think anyone's really answered my question but you've hit the closest to it I think, so I'll rephrase it in the hopes that you can clarify it for me: what do we _need_ Category Theory to do that the other branches of math cannot do either in the absolute sense, because its core axioma contain something that other branches of math don't, or in the practical sense of something it VASTLY simplifies in application? On the theoretical example, I could tell someone that using graph theory, I could prove things about visiting nodes and vertices that I couldn't simply with tree theory. On the practical example, if someone came to me and said, "Why do I need abstract algebra"? I could point out to him that if I had a vehicle with a really complex set of tires, that if you could prove an isomorphism of permutations of the tires was a group over the set of permutations, you could create a rotation schedule that would move every tire to a different spot of the vehicle on each rotation, maximizing their useful life - I don't think there's a LESS abstract branch of math that could do this. What would be an instance in either case for graph theory?