When I got my boys, I had a bunch of cats around my apartment. Since they were too young to get their shots, we made the boys a little corner to isolate them from any possible sickness. The cats would look over them and just watch them. After the boys got their shots, we let them walk around the apartment and the cats actually got a long with them, or stayed away. Our two biggest cats would play with them. Since the boys were younger, their bites weren't so vicious and all four of them would just jump around each other. One of our cats didn't like the boys, so when one of them would try and play with him, he would sit there and just paw at them. The boys loved it lol.
What I will say, though, is my pups were not very good with kittens. My brother-in-law had kittens with one of my cats, but the mom developed mange, so I would have to bottle feed them, and one of my boys walked over to me and seemed to just want to sniff, and then he opened his mouth and lunged forward. I pushed him away quick, but yeah, pits and baby kittens didn't do well.
I think if the pit is young when the cat is introduced, there shouldn't be a problem. Most cats tend to stay away from things they don't like anyway.