I don't have any cats myself, but my dog loves cats. My groomer rescues cats, so there are lots of cats in her shop, my poodle greets them all like long lost friends every time he arrives there. One of the cats always crouches by his legs while he's being groomed, and my dog is very careful, making sure not to step on the cat by accident and hurting it.
A friend of mine has 3 cats and a dog. Whenever the cats fight, her dog will act as referee breaking up the fights, barking and nudging them away from each other. It's an amusing sight!