A Note on the Non-Existence of Functors

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.