Is it possible for a cat to have no carbohydrates at all?

It is not possible for cats to have a carbohydrate-free diet. Cats and dogs get some carbohydrate from protein (gluconeogenesis) so that they have glucose and other sugars for important functions, such as energy for the brain. Carbohydrate in the form of fiber is also important for gut health – both for prebiotic functions (e.g. oligosaccharides and bulk volume) to allow gut contents to move and avoid constipation.