The main result concerns a bicategorical factorization system on the bicategory Cat of categories and functors. Each functor f factors up to isomorphism as j, p 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.
Keywords: factorization system; bicategory; fibration; final functor
2020 MSC: 18B10, 18D05
Theory and Applications of Categories, Vol. 37, 2021, No. 29, pp 964-978.