Cats are purchased from the cat crate next to the cat trader. Cats are an in game cosmetic that have no effect on the game; they are not upgrades. Cats will roam around your home farm and, much like a real cat, provide absolutely nothing. Cornucopias and can spent to be reroll a cat into another cat of the same tier or to "upgrade" 3 of the same cat into a random cat of the next tier.
Can't be rerolled because there is only 1 type of cat. Upgrading costs is 5 cornucopias
Reroll cost is 3 cornucopias