  We establish the following non-abelian analogue of the Fundamental Theorem of
Projective Geometry: the natural map from ${\rm{Aut}}(F_n)$ to the automorphism
group of the free-factor complex $\mathcal{AF}_n$ is an isomorphism. We also
prove the corresponding theorem for the action of ${\rm{Out}}(F_n)$ on the
complex of conjugacy classes of free factors.
