If you have a pitbull, you can have a cat, but there are certain things you should think about before bringing a cat into your house. These factors include your dog's temperament, energy level, socialization, and whether or not they have a powerful prey drive. This is since high-energy dogs, dogs who hadn't been socialized with cats, and dogs with a high hunting instinct could be deadly to cats. However, this description may not apply to all Pitbulls. If your dog is well-behaved, has a low hunting instinct, is well-trained, and has already socialized with cats, a cat will fit nicely in your home.