Sure, but it also has nothing to do with their chromosome structure. It has a lot to do with their gender expression, in the end.

> A woman is, quite simply, an adult human female.

So an adult human female (XX phenotype) who is taking masculinizing hormones and thus has a beard, body hair, a heavy voice, and perhaps has had his breasts surgically removed, or even had penile reconstruction surgery, is, in your opinion, a woman?

If he is not naked and you do not have a genotypic test result, how would would you know? Do you think a woman seeing him in a women's locker or in a women's bathroom would feel comfortable? Or would she feel more comfortable with a male that has a female body and clothing presentation (say, Caitlyn Jenner)?

Also, your definitions of course leave no room for people with various biological conditions that leave them with an uncertain biological sex - hermaphrodytism, XXY genotype, chymerism (multiple genotypes in different tissues), testosterone resistance (natural female phenotype despite a male genotype) etc.

> So an adult human female (XX phenotype) who is taking masculinizing hormones and thus has a beard, body hair, a heavy voice, and perhaps has had his breasts surgically removed, or even had penile reconstruction surgery, is, in your opinion, a woman?

Yes. She's a woman who has taken masculinizing hormones, and had cosmetic surgery. She is not changing her sex. She remains female, and is therefore a woman.

Consider this: the women athletes who have doped with testosterone, did they become men? No, of course not. What if they got breast cancer and had to have a double mastectomy? Also no - they're still women.