When something is stated categorically, it's asserting total certainty or rejection, leaving no room for doubt. He issued a categorical denial of ever having accepted bribes.
Pro Tip 2/3
Serious Tone
Using 'categorical' implies a serious and firm tone, often used in formal situations or arguments. I offer my categorical assurance that the project will be completed on time.
Pro Tip 3/3
Strong Emphasis
Use 'categorical' to emphasize the strength and decisiveness of a statement, refusal, or approval. The manager's categorical approval signaled a major shift in company policy.