What category does the word "no" fall in to? Is it a negative adverb?
You might call it a negative response, or simply a negation.
- A negative response is simply denying something.
- A negation re-qualifies what it is associated to as the opposite.
So, if you say:
No, I do like cheese.
then you are giving a negative response. That means you are responding by rejecting someone else's claim that you don't like cheese. (Their claim might have been, "you don't like cheese?".)
Or, if you say:
No big deal.
then you are saying that what you have just done is not a big deal. That is negating the phrase "big deal", so we would call this a negation.
As for if it can be an adverb, it isn't.