Categorically and set

Hi, I know it's simple word but somehow 'm not getting well the meaning for "Set something" here ...

Can you write here example with "Categorically"?
I don't see a lot of diffrence between "Unequivocal" ( A word I saw before on the book) and "Categorically" as it appears here-

Rouse sketched out a memo, an update of his earlier strategic plan, that set forth
two alternate paths for Obama in the year ahead: one if he
was categorically rejecting a presidential bid, the other if he
wanted to keep the door ajar, however slightly.

Thanks ...