English ain’t my first language, but I’ve often seen “cleaning” being used without a direct object, either because it’s implied (“put away after cleaning”) or because the action is meant to be generic and not limited to a specific object (“I’m going to do some cleaning”)… in this case it could be both (specific: the cat itself, or specific parts thereof, generic: the cat itself, the other cat, the coach, anything within reach; cats can often get carried away, when cleaning).