A domestic scene:
I’m in the bathroom. I leave the door open a crack so Buster can get in, because he doesn’t like being locked out, because he wants to be brushed. He lifts his front paws to shove the door open; I shove it back to just barely being ajar to spare my brother (whom I have just greeted, as I do when I rise in the morning if he is awake) a view of my ample fundament, just in case he wanders by in search of tea.
I take out the metal tined brush and brush his back a couple of times, and he goes straight back to the door, mews, lets himself out.
“Do you want the other brush?” I call softly through the door.
He pushes the door open again and doesn’t come closer until he sees the brush he wants, which makes him purr as I brush hard under his chin (what he wanted in the first place.) I brush him, conclude my business and he jumps up on the toilet. (In this household, toilet lids are kept closed when toilets are not in use.) I brush him some more and when I’ve collected a fair bit of fur, I stop and wash my hands.
I say to him, “You know the brushing is all done when I wash my hands. If you want a treat, jump down.”
He looks at me and mews. I point at the floor. He jumps down and I follow him into the kitchen and start an abbreviated training session, since he isn’t much into it.
Buster has very definitely learned what ‘brush’ and ‘treat’ are, is iffy about ‘jump’, ‘up’ and ‘down’ and ‘all done’ out of the context of training (but getting it from time to time), has started to respond to hand directions without a treat, and the only thing that remains is to figure out how to get him out of my chair downstairs….
Training is all about ‘things the cat would have done anyway’, you’re merely encouraging the animal to do it both faster and in a specific order. That, as they say, is all, until five minutes later, when he’s decided he hasn’t played ‘catch the treat’ enough and initiates another training session, (bangs my left shin with his forehead is the signal) which is adorable, because he wants more treats and knows he has to jump around and make a total fool of himself to get them, and he’s okay with that.
He asked for another training session a half hour after THAT. What a cat.