Legal Question in Real Estate Law in California

I think this is a question best asked of the landlord or management. The concept is not set forth in statute and may vary from property to property. I think courts tend to divide non-human members of the animal kingdom into livestock (including horses), pets, wild animals, bugs and microbes. That would tend to put goldfish, small birds and hamsters in the pet category, but for apartment-management purposes, the landlord may be concerned about where the "pet" will be going to the bathroom and how much noise it might make. If it's quiet and poops on the cage floor, maybe it's not what they mean by a pet. You'll just have to ask,

It is entirely up to the landlord what he will allow. Negotiate a deal with him.

A landlord may be even more hesitant to allow fish, because that involves aquariums and aquariums are notorious for leaking. You had better speak to the landlord and work out an arrangement.