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Variation on a comprehensive theme
Theory and applications of categories, Tome 37 (2021), pp. 964-978

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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.

Publié le :
Classification : 18B10, 18D05
Keywords: factorization system, bicategory, fibration, final functor 
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     author = {Ross Street},
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Ross Street. Variation on a comprehensive theme. Theory and applications of categories, Tome 37 (2021), pp. 964-978. http://geodesic.mathdoc.fr/item/TAC_2021_37_a28/