I want to train my cat to enchance his speed is their special trainning for this like runni g down and up the stairs case

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I want to train my cat

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So you want to train a cat. Good luck with that.

Someone is having cat races someplace?. this I got to see.

Cats are very trainable if there's a reward (a constant reward).
I trained my cat.
It takes more knowledge and patience than I feel like going into. You're on your own!