Not trying to be that guy, but it's urea, which breaks down to ammonia due to microbial action once it's out of the cat. If a cat is pissing ammonia, it has big problems and needs to see a vet.

Other contributors to awful cat piss smell are mercaptans, the same compounds responsible for the scent of skunk spray, and pheromones and fatty acids released when the cat is spraying versus normal urination. It's all compounded by cats being adapted for arid environments so their urine is much more concentrated than human urine.

I love cats but they're gross little fuckers sometimes.