We consider several cases of non-existence theorems for functors. For
example, there are no nontrivial functors from the category of sets, (or the
category of groups, or vector spaces) to any small category. See 2.3. Another
kind of nonexistence is that of (co-)augmented functors. For example, every
augmented functor from groups to abelian groups, is trivial, i.e. has a trivial
augmentation map. Every surjective co-augmented functor from groups to perfect
groups or to free groups is also trivial