If you look through past posts, there's lots of them on hedgehogs/other animals, including cats.
A lot of people recommend not letting hedgehogs near cats, dogs, any other predator animals. There's no benefit to it to either animal, and plenty of dangers. A lot of times, the cat/dog/etc. is afraid of the hedgehog, but you never know. It's very easy for them to hurt the hedgehog just by pawing at it, or trying to play, much less if they're actively trying to attack it. Plus, people have mentioned that there's diseases/parasites that can pass from one animal to another, even if it doesn't hurt the original animal it came from. An introduction between a cat and hedgehog would just be a bad idea.
However...As long as you have a sturdy cage with a top on it, and the cat isn't harassing the hedgehog in its cage, it'd be fine if the cat was in the same room. I would try to keep the cat out of the hedgehog's room at night though, in case it would end up scaring the hedgehog and keeping it from coming out of its hideaway.