Given a functor $F$ which is not full, there may be arrows $f : FA \to FB$ which are not of the form $F \tilde{f}$ for any $\tilde{f} : A \to B$.
I have been calling these arrows "nonstandard", but I am curious if there is an accepted terminology for them. In particular, it would be nice to have something to google to see if any of my results are corollaries of other theorems.
Thanks in advance!