So I'm confused here, and I can't find any satisfactory definitions online for this... So in this text that I am going through, it says the following:
For a vector bundle V on a smooth curve C and a subspace $K \subset V_p$, where $V_p$ is the fiber of V at a point $p \in C$, ....
I have dealt with fibers of morphisms... But how can you have a fiber of a single object at a point?... Without a morphism... I'm sorry if I'm not clear enough... I'll give an example.
If X and Y are topological spaces and $p: X \rightarrow Y$ is a continuous map, we say that $p^{-1}(y)$ is the fiber of p over y...
And I definitely get this definition... But the case above is dealing with a morphism between objects, and in the set-up with the vector bundle, it's literally just the fiber of a vector bundle at a point on a curve...
What exactly am I missing here?