What mental illness does Tyler Durden have?

What mental illness does Tyler Durden have? Without knowing much about schizophrenia or dissociative identity disorder, one might assume Tyler Durden was an alternate personality as opposed to a hallucination, based on the text.

Without knowing much about schizophrenia or dissociative identity disorder, one might assume Tyler Durden was an alternate personality as opposed to a hallucination, based on the text.
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