What state or city law allows HOAs to mandate how many cats a home owner may keep?

I understand that a HOA Board has jurisdiction over what happens in community common areas, but I do not understand how they can have any authority over what happens inside what is private property, over which they should—in my estimation—not have the slightest vestige of control or the ability to tell home owners what to do about anything. I am thinking specifically about the limitations on the number of pets, Again, I can understand this… if it applies to eg: dogs that go outside and can leave poop and/or be noisy, but, for cats which remain solely indoors, I do not see how they can mandate anything. Surely, what happens inside a privately owned home concerns only the home owners and no one else?!