Can my cat live on a vegan diet?

There are vegan diets formulated for cats. However, I think it's important to know that cats are obligate carnivores. It's challenging to adequately control their nutrition on a strictly vegan diet. Even on a vegetarian diet, it becomes difficult to formulate a diet for cats. There are some on the market. However, studies that have been done on those diets show that their labels are often inaccurate, and they are deficient in the amino acids that are necessary for obligate carnivore bodies. They've also shown that those diets are often contaminated with mammalian DNA. So there are animal products in those diets.

I would not recommend that you feed either a vegan or a vegetarian diet to a cat unless there is a medical reason to do so, and your veterinarian has recommended that. If that's the case, then I would only use a prescription diet as these are frequently tested for contamination, and they've been formulated for cat-specific amino acid requirements. Or I would work with a veterinary nutritionist to formulate a vegan diet that you then home cook for your kitty.