Domestic cats are what are called obligate carnivores. This means, unlike dogs, they are true carnivores. Meat must make up the majority of their diet and they have an extremely difficult time digesting vegetable matter.
Some vegetarians and vegans acquire pet cats and immediately want to switch them to a vegan or vegetarian diet for cats. Sadly enough, these diets, and foods, do exist, and are marketed for cats through specialty stores that cater to vegetarians and vegans.
Regular dry cat food, the stuff sold through grocery stores and department stores, is already considered a poor source of meat for cats. Indeed if you look at most dry cat food ingredient lists you will see corn as a key ingredient. Corn is hardly a good meat source. It is hard for cats to digest and is a well known cause of allergies for both cats, and dogs.
Most vegetarians are against eating fish and dairy, but a few find these acceptable and make up for not feeding chicken and other animals to their cat, but feeding it fish or dairy. These people fail to note that while cats love fish and dairy neither are natural for them, and both can cause problems.
Fish, especially Tuna is high in mercury and PCB's. Salmon is high in Calcium, and like the problems with calcium in milk, contributes to urinary tract problems. Even boneless fish are high in phosphorus and magnesium, both of which contribute to urinary tract problems. Additionally most cats are lactose intolerant so dairy products cause tummy upset and even diarrhea.
Cats need other vitamins and minerals not found in vegetarian, and certainly not in vegan, diets. These include taurine, arachidonic acid, Vitamin A, and B12.
Taurine is necessary in cat food and if lacking can make the cat blind. Even dog food does not contain sufficient Taurine for cats.
Arachidonic Acid is a fatty acid that cats require. It is present in eggs in only a small amount so meat is an ideal source.
Vitamin A is found in some vegetables but cats cannot absorb it unless in the retinol form which only comes from meat sources (particularly liver) and is also limited in eggs.
Vitamin B12 can only come from meat sources as cats cannot synthesize their own.
Protein is the biggest concern. While vegetarian, and vegan, cat foods claim a certain amount of protein, if it is in vegetable matter it is very hard for cats to digest. As such a cat must eat a lot more food to get its full needs of protein.
Only one of these animals is a vegetarian.
Cats who are on vegetarian or vegan diets really are not vegetarians or vegans, they are just forced to eat that kind of food and if given the opportunity would certainly prefer to eat meat. Cats are natural predators, they would love to kill and eat a mouse, bird, or anything.
In the United States a pet food must qualify under the AAFCO (Association of American Feed Control Officials) regulations. Unfortunately these regulations are not terrifically high. These regulations permit the use of cancerous tumors, worm infested organs, and even road kill and euthanized animals (the later two will show up listed as meatmeal on an ingredient list). As such it is no surprise that AAFCO regulations have approved some vegetarian and vegan cat foods.
It is up to you, the owner, to feed your cat correctly, not only should they not have foods that contain corn as the main ingredient, they should not be fed vegetarian, or vegan cat foods even if the food administration approves them for cats.