My parents had an Umbrella Cockatoo and a couple of cats when I was growing up. They usually got along fine. The Cockatoo was kept in a big cage that had an area on top for him to perch and play around. One day, one of the cats decided to check out the top of the Cockatoo's cage, while the Cockatoo was out.
The cat was up there all of five seconds. He never seemed to have much interest in going up there again, either. 