Simple question: should the tagging of a question cover answers?

Suppose I asked a question about a mathematical problem and in the answers contained for example:

- pointers to literature
- algorithms
- examples
- counterexamples
- $\cdots$

should the tagging of the question be updated to cover what is in the (correct) answers, resp. is it already or should it be possible to tag questions directly?

afteran answers is posted it becomes clear that the question is related to infinitary combinatorics and in the question the relation to this are is not clear, then the corresponding tag should be given.) $\endgroup$