I love my cat.  They're often valued by us for companionship and their ability to clean up mice and such.
I used to have a cat, I do miss having a cat around the house
They are normally called house cats when kept as indoor pets, or just cats when there is no need to distinguish.
bur are cats truly domesticated like dogs?
Well under controlled breeding, they can be bred and shown as registered pedigree pets.  It's actually known as a "Cat Fancy".
Cat Fancy? is that what they call the process of breeding cats?
Cat Fancy
Cat Fancy was the name of a popular North American monthly magazine dedicated to cats, owners of cats, and breeders of cats published by I-5 Publishing.
In late 2014, I-5 Publishing announced that the monthly magazines "Cat Fancy" and "Dog Fancy" would be cancelled, and replaced with alternating bimonthly issues of "Catster" and "Dogster" beginning in February 2015.
The magazine.
The first issue was published in 1965. Since then, each issue has been dedicated to a certain
Exotic felines as pets
A pet exotic feline, also called pet wild cat or pet non-domestic cat, is a member of the Felidae family (excluding the house cat and hybrids thereof) kept as an exotic pet.
Definition and differentiations.
Hybrids of the domestic cat with non-domestic species (e. g. the Bengal cat or the Savannah cat) are not normally considered wild cats. While this distinction is often overlooked in the media and in the public eye, such cat breeds (especially the F5