-Dave Lister to Captain Hollister ("The End")
Lister smuggled Frankenstein on board Red Dwarf after shore leave on Mimas, one of the moons of Saturn (Mimas in the television series; Miranda in the novels). She is described in the novel Infinity Welcomes Careful Drivers as one of the most expensive and healthiest cats he could find, as he knew the danger of an unhealthy animal aboard a spaceship, and that her name was a show name inspired by the classic horror character. Frankenstein was pregnant by a 'big, black tom on Titan', and Lister took good care of her, giving her milk while daydreaming of his plan to buy a farm in Fiji and live there in bliss.
Holly detected Frankenstein's presence. Frankenstein was discovered by Captain Hollister, Red Dwarf's commanding officer, when Lister took pictures of himself with the cat and sent them to the onboard photography lab. ("The End") Hollister demanded Lister turn over the unquarantined Frankenstein to the ship's medical staff in order to dissect it, since it could carry disease that could spread to the crew as well as get into the ships machinery. He tells Lister: "Lister, a loose animal aboard this ship could get anywhere. It could get into the air ducts. It could get into Holly. You know, a little nibble here and a little nibble there, Lister, and before you know it we're flying *backwards*. Now I want that cat, and I want it now!"
- Hollister mentions an incident on the space ship Oregon where a disaster was caused by rabbits. We can only imagine the massive amount of damage that can be done by these creatures.
It was Lister's refusal to turn over the cat that saw him sentenced to eighteen months in stasis, where he was safely shielded from the radiation leak that killed the rest of the crew. The only other survivor was Frankenstein, who was safely hidden in the cargo hold, away from the radiation.
Frankenstein eventually gave birth to her kittens which bred, and over three million years her descendants evolved into an intelligent, humanoid Cat species, Felis sapiens, the last known individual of this species aboard Red Dwarf being Cat.
Frankenstein was revered by her Cat descendants as the "Holy Mother". Her basket also received special significance for the Cats, as it contained the last instructions of Cloister the Stupid, the Cats' god. These instructions were actually Lister's laundry list. ("Waiting for God") It can be assumed that due to the fact that Lister was known as "Cloister the Stupid," Frankenstein didn't think very highly of him.
Her name's inspiration is mentioned in the dialogue of Series V's "Quarantine" in which Cat uses the name to insult Kryten causing him to point out that Frankenstein was the name of the creator and not the monster. He elaborated that "it is a common misconception held by all truly stupid people." It is in fact a common misconception in popular culture.
Deb Lister's Universe
However, Kristine Kochanski discovers her inside Lister's shirt while boarding Red Dwarf. She then sets about following regulation and disintegrating it at the Waste Disposal, but she does not have the heart and ends up keeping the kitten. She is later discovered and thus Kochanski is sent into stasis just as Lister was in our dimension thus making her the last human alive alive after their radiation leak.
Frankenstein being a kitten leads to questions about how she could be pregnant, assuming that the depiction is mostly accurate in our universe as well, and that an alternate Cat is shown to exist from that dimension. ("Ouroboros", Series VII)