cat ‧ e ‧ gor ‧ i ‧ cally /ˌkætəˈɡɒrɪkli, ˌkætɪˈɡɒrɪkli $ -ˈɡɔː-, -ˈɡɑː-/ BrE AmE adverb
in such a sure and certain way that there is no doubt
categorically deny/refuse etc something
He has categorically denied his guilt all along.
Can you state categorically that her death was caused by lack of food?