I hear it is very difficult to train cats (to obey) compared to dogs. I once saw a trained cat act on David Letterman but that was about it
Dogs will obey because they are people-pleasers, and also because as a species they have been domesticated much longer. Cats will not obey, but they will show off in exchange for treats of some kind. I trained a male cat to do tricks for bits of cheese, and trained two female cats to perform tricks in exchange for brushing their fur, which they loved. This trainability came in handy when they became old and developed illnesses requiring them to swallow pills every day.
My one cat could recognize over 90 words or figures of speech. She could exercise a lot of control over her environment and preferences for activities and food, because I would do things like let her choose which flavor treats she wanted. This involved letting her sniff-test as I announced the words "chicken", "fish" or "beef" every time, until she would respond only to my saying the name of the treat packages, and she would then touch the one she wanted with her paw. After many months of repetition of the mechanics of the house she could also respond to "helpful suggestions", such as "bump" -- to bump the door with her head if it was appeared closed but was not latched and she wanted to go through. This did not feel like obedience to her, it felt like I was assisting her to give her what she wanted.
The above video has been cut and spliced several times, since cats will only perform for just so long before they walk away, growl, scratch or bite; so a good trainer builds up their tolerance over time instead of demanding more than they are willing to give. You can also see the cat's tail whipping from side to side in some scenes, which is cats' warning that they've about had enough.