IPA: /ˌkætəˈɡɔrɪkli/
KK: /kætəˈɡɔrɪkli/
In a clear and definite way, without any doubt or ambiguity.
She categorically denied the accusations against her.
Categorically → It is formed from "category" (from Greek "katēgoria", meaning a class or division) and the suffix "-ically" (meaning in a manner relating to). The word "categorically" means in a manner that relates to a specific class or category, often used to express something in an absolute or unequivocal way.
Think of a 'category' as a specific class or group, and remember that 'categorically' means expressing something in a clear and absolute manner related to that class.