I think it depends on the cat. If the cat tends to just lay around all day, you're most likely not going to be able to train it to do anything, lol. Maybe you can associate it to understand the crack of a can opening means suppertime is here, and she'll come running to the kitchen. But that's it, lol
But if said kitty is always "up in your business," always interested in what's going on, always THINKING, then she could be a good training prospect. I have one of those, Buffy, a high energy little girl who has a HIGH need for mental stimulation. Kind of a nightmare, actually, lol. But anyway, it's easy to train her, but I haven't actually done that. The most I did was to teach her to "beg" for her favorite treats, but I ran out of the bag before getting past the stage where she'd place her front paws on my hand. Then it'd be a long while before I'd get another bag, because this treat that she loves so dearly is crappy stuff, and I don't want to fill her system with junk. So when I get another bag eventually, she's long forgotten anything I've taught her. But I just "teach" her by simply watching her life her life. Buffy's naturally smart; it's fascinating watching her stare at something with her head tilted, then reaching out a paw to fiddle with it (usually to push something off a shelf and observe the reactions of people around her, or prying a door open and slipping out through the crack). Buffy, due to her high stimulation needs, is a fantastic escape artist, a door darter (my girls are all indoor cats), and she knows when my dad gets home. Around that time, about 6:30 or so, she'll start getting more, uh, annoying, vocal and invading your space. She tend starts hanging around the back door, and just lounging out of sight. Dad will come home, open the door, leave it open a bit too long, and Buffy's gone, dashing through the grass.
Actually, I think I can say I taught her to "come." Not like a dog, mind you, but if she got out, I taught her to come when I stood out on the front steps and called her. I initially would go out with a can of food when she'd sneak out, and just crack it open. Buffy would come running, because she knew I'd feed her. Then it was no time at all when I'd just have to call her and she'd come running, and I'd feed her anyways. Gotta reward her every time for responding to me, and give her a reason to want to come inside (even a few times of NOT giving her food will give her pause in the future, to think about the likelihood of whether or not she'd get food if she came back to me)