APBT and cats
Personal history, 1 pitbull (mine) - good with cats, 1 pitbull (my friends) - not good.
My APBT Indy was excellent with the cat, raised with them; however he could play a bit rough -they had a game where he made the cat "squeak", but would stop play when told to stop "squeaking the cat". The cat apparently didn't find this offensive as much as I did, as he never left the room when this game was being played. Indy was cold, no dog aggression, but he had high prey drive and would hunt rats, 'coons, and 'possums.
My friend's APBT Lucy has removed a piece of a cat's tail from under the bathroom door (where the cat was eating for her safety), and still at the age of 10 whines that high pitched pitbull scream to get at any cats, family or not. Lucy WAS RAISED with the cats in question. Lucy is high dog aggression, and low on tolerance for family dogs. My friend is a highly skilled dog trainer, specifically with aggressive dogs, so IT'S NOT all about the training.
If you are getting an adult APBT, make sure that it has been evaluated with cats, and yes, ask to see it's interaction before you bring it home.
Training only goes so far, breed tendencies can come through.