White is a somewhat complex color, since it can take a few different forms.

White-spotting:

The most common form of white found on cats is white spotting, which is where a cat has white markings on their pelt. The white spotting allele (represented by Ws) is dominant to the non white spotting allele (ws). However, white spotting uses something called incomplete dominance. It's a bit similar to codominance (discussed on the page about ginger cats), but also a bit different.

A cat with the genotype ws/ws would not have any white on them, and would be a normal single colored cat.

A cat with the genotype Ws/Ws  or Ws/ws would have white spotting on them, and THIS is where incomplete dominance comes into play. A cat with the genotype Ws/Ws would have 50-100% white spotting on them, while a cat with the genotype Ws/ws would only have 1-50% white on them. It's called incomplete dominance because in its heterozygous form, the white-spotting isn't fully expressed the way it is in its homozygous dominant form.

Here is an image for reference, also from Messybeast!

Also, here is an image talking about the different types of bicolored cats, and their names, from Messybeast:

Also, a cat that is homozygous dominant could potentially be a white cat! A cat with 100% white spotting would be born completely white, with a patch of their original color on their head. However, this is extremely rare.

Dominant White

The second form of white found in cats is dominant white, which is only found in purebred/pedigree cats, so if you want this gene to be implemented in your Warriors fanfiction, you MUST have some of your cats come from kittypet ancestry. Dominant white is a form of white that causes a cat to become fully white, regardless of their other genes. Since this gene is (obviously) dominant, a cat would need the genotype Dw/Dw or Dw/dw in order to be a white cat. This means that a cat cannot be a dominant white cat unless they get that gene from one of their parents.

A dominant white cat is born with a dot of color on their head, which fades away over time. Dominant white cats with blue eyes have a high chance of being deaf.

Albinism

The last form of white in cats is known as albinism, which doesn't just happen in cats. Albinism is a condition found in many animals, where there is a lack of melanin (pigment) in a certain animal. A cat with albinism would be a completely white cat with either pale blue or pink eyes. Unlike dominant white cats, they're born completely white due to a lack of pigment in their bodies. Albinism is a recessive trait, and cats with albinism are pretty light sensitive, so keep that in mind if you are planning on including a cat with albinism in any Warriors fanfiction.

So that covers the three types of white found in cats!