Which of the three words can be applied to talk about people, their personality?
Can I say: He is a categorical (intransigent/uncompromising) person?
What is the most common word to talk about this kind of personality type?
If I were a native speaker of English, I would never shut up. :-)
What kind of personality type?
I wouldn't use categorical to describe a person, but rather something that they say.
'An uncompromising person' is OK.
I might describe someone as intransigent, but I doubt I'd say an 'intransigent person', although there's nothing wrong with it.
I am not a teacher