Stomp Cats are not designed to accommodate an internal battery. They therefore come with an external battery box that makes it easy to use a 9V battery (included).
Of course, the most convenient way of powering a pedalboard is from the mains. Not all models are equal, far from it, and from personal experience I can recommend the two references below. These power supplies have isolated outputs that make them silent. One offers remarkable value for money, while the other can power a pedalboard stuffed with greedy pedals.