I think you can do a rotation schedule for the tires using other techniques that are more concrete than group theory. If you think about the quadratic formula,

I think you can do a rotation schedule for the tires using other techniques that are more concrete than group theory. If you think about the quadratic formula, the Babylonians used it without having a way to write down the equation. But, having mentioned the caveats, I think the answer is that we don't have a nice example yet for category theory. I personally think that the key application of category theory will be in quantum mechanics and in reactive behaviour of programs and formal methods around that. So, for example when you prove your program does something rather than testing it 1000 times. (You'll have to test it in any case due to things like implimentation bugs.)