  The main result concerns a bicategorical factorization system on the
bicategory $\mathrm{Cat}$ of categories and functors. Each functor $A\xra{f} B$
factors up to isomorphism as $A\xra{j}E\xra{p}B$ where $j$ is what we call an
ultimate functor and $p$ is what we call a groupoid fibration. Every right
adjoint functor is ultimate. Functors whose ultimate factor is a right adjoint
are shown to have bearing on the theory of polynomial functors.
