Is it ethical for a vegan to own a cat as a pet since these animals require meat to live?

Speaking as someone who has simply abstained from eating meat for over half my lifetime, now, and has greatly restricted the use and consumption of other animal "products"? I do not feel it is [i]un[/i]ethical for to me give a cat a home, and feed that cat what is necessary for his or her health and ultimately...survival. It has been somewhat of a moral dilemma for me at times, though.