"Catnaps" are catnaps. They aren't really naps at all. Your cat would be so still, unmoving, and you'd begin to wonder what's so sweet about his dream, if you could possibly join him there, or have one yourself. But make one noise and he's instantly awake.
When cats are asleep, however, they really are. Azi does not want me touching his furry tummy, and I can get swiped at just for trying. But when he starts to snore, then I'm in luck :) Actually, you could just about do anything to Azi when he's dreaming up his sexy girl catfriends slinking in and out of his vision. You could push him around your bed to make room for what's left of it enough to get some decent sleep, or you could shove him off the bed altogether and he'd still be out cold, sprawled belly-side-up on the floorboards and outsnoring my roommate.