Cats usually are associated with the hidden mysteries of the female, being lunar rather than solar. (The Egyptian cat-goddess Bastet also was the moon goddess).
So the cat represents the hidden and also the subconscious aspects of the feminine. She can be a symbol of cruelty (cats, as hunters, in their devouring aspect), as well as a symbol of liberty (cats are difficult to catch, can hardly be trained, etc.). In the Middle Ages, cats were related to Satan. They were the companions of witches.
As a symbol, the cat can also represent stealth, desire, and laziness.
Many civilizations have legends of lion or cat people. These may refer to an actual humanoid cat like race from the Constellation of Lyra. Therefore, a cat can be used as a symbol for the Lyrans. This is consistent with ancient myths that tell of fights between serpents and cats or eagles, which is a symbolic representation of the fights between Sirians, depicted as serpents, and Lyrans, depicted as eagles or cats. (See: Earth's Galactic History for more information).
Note that at least two authors, though, refer to Sirius as the origin of the lion and / or cat people, while yet another one refers to Regulus.