The short answer is No!
Cats are obligate carnivores, which means that they cannot derive all their essential nutrients from a plant-based diet.
In particular, cats are unable to produce the amino acid taurine and the fatty acid arachnidonic acid, which can only be found in meat. Cats fed on plant-based diets are also likely to be deficient in Vitamin A.
Taurine is involved in heart health and cats fed on a taurine-deficient diet will suffer from a condition called dilated cardiomyopathy, which causes the heart muscle to become thin and floppy and unable to pump blood around the body effectively.
Taurine deficiency also causes retinal degeneration and eventually blindness, hair loss and tooth decay.
Arachidonic acid is involved in the growth and repair of muscle, as well as brain development and health. Deficiency can also cause liver disease, skin problems and problems with blood clotting.
In conclusion, cats should always be fed a meat-based diet and are not suited to vegetarianism. Feeding a cat a vegetarian diet will cause serious health problems and owners could potentially be prosecuted under the Animal Welfare Act.