categorically

Hello sir, In what context do we use the word “categorically” ? When i look up the dictionary, it says “without doubt, unconditionally”. Yes i know this meaning but in real world, there are lots of words almost similar to this meaning and are they interchangeable? So please let me understand its real concept with some examples. I would be so grateful to you if you kindly spare some time to help me clear my doubts.

That’s a very wide ranging question. Sometimes this word is interchangeable with others, but it depends on the context.
Perhaps you can provide some examples and we’ll tell you if they are correct uses.

1.The constitution categorically says that people of the country are sovereign.
2.He categorically refused to take part in the contest.
3.He has categorically denied any connection with the mysterious incident.
4.This smear is categorically false and has no basis in fact.
In the above sentences, what does the word ‘categorically’ really mean? The dictionary says that it means ‘in an unqualified manner’. This make me even more confused and i still don’t get it. please let me know its meaning in the above context.

These seem pretty clear to me

1.The constitution categorically says that people of the country are sovereign.
The constitution says without a doubt that people of the country are sovereign. There is no exception to this in any way at all.

2.He categorically refused to take part in the contest.

Without a doubt, he refused to take part in the contest. He refused to take part in it in any way at all.

3.He has categorically denied any connection with the mysterious incident.

Without a doubt, he has denied any connection with the mysterious incident. He has denied having a connection in any way at all.

4.This smear is categorically false and has no basis in fact.
Without a doubt, the smear is false. It has not basis in fact in any way at all.

To me, categorically has the same meaning in every one of your sentences.

As a side note, and please ignore this if it is confusing, the philosopher Kant had a term he called “the categorical imperative.” This means something we are impelled to do, something we must do, no matter what, unconditionally. He thought one categorical imperative was “Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.” To me this sounds a lot like “Do unto others as you would have them do unto you.” Sounds pretty good to me.