Variation on a comprehensive theme

Ross Street

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.

Published 2021-09-06.

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