The Purina company that makes popular brands of cat food sponsors cat conventions and cat adoption events, and I did see a trainer with performing cats on stage at one of them. She used bits of food as performance incentives for their circus tricks of jumping through hoops, leaping across spaces and walking on narrow edges, etc. But I once had a house cat who was so grateful for being rescued that she performed a number of things as we trained her over time, such as choosing which flavor food she preferred on a given evening, opening doors, returning to the house when called, giving "kisses", a rudimentary understanding of quantities from one to four, etc. We used love, brushing and petting to encourage her.
I actually saw a cat show once too.
my daughter worked for a place that trained animals for Hollywood movies. She actually helped with all the animals on the “We Bought a Zoo” set. She said of all the animals, house cats were the hardest to work with.