categorical

If someone accuses you of stealing their lunch and you give a categorical denial, it means that you absolutely deny having anything to do with the theft. Categorical means absolute, unqualified, unconditional.

If you ask a girl to marry you and she says maybe, you might be able to persuade her. If it's no, you might still have a chance. But if she gives you a categorical no, she will never change her mind. Less often, categorical is used to describe something that is part of a certain category or group. A Doberman at the Westminster Dog Show might be the categorical winner, meaning it is the best Doberman but the winner of the show.