Animal mummification falls into four basic categories:

CULT ANIMALS

The most famous examples being the Apis bulls, and other bull cults, which survived the whole length of Egyptian culture.

Here we have a sarcophagus that a cat or a similar animal would be placed in.

BACKGROUND ON DOMESTIC ANIMAL MUMMIES, AND VICTUAL MUMMIES

and victual mummies - mummified meats, were interred(placed deep among) along with the mummy of persons of power as part of their grave goods to be food and companionship in the afterworld. Domestic pets of many species, gazelles, monkeys, dogs and cats, were mummified after their natural death, and placed in their owners' tombs.

This is what a mummified cat looks like outside of a wooden coffin.

Votive mummies were offerings to the gods and occur only late in Egyptian history. All kinds of animals were offered, the most abundant being cats, mongeese, ibises, hawks, vultures and crocodiles. Unfortunately, votive animal mummification is a subject which has had few serious studies, despite the abundance and popularity of the relics.

Here is a closer picture of a cat coffin. The animal inside probably didn't belong to a wealthy person, for there are no jewels or gold on the coffin.