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2021•Theory and applications of categoriesOpen access

Variation on a comprehensive theme

Ross Street

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Abstract

The main result concerns a bicategorical factorization system on the bicategory Cat of categories and functors.Each functorwhere 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.

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The main result concerns a bicategorical factorization system on the bicategory Cat of categories and functors.Each functorwhere 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.

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Available abstract

The main result concerns a bicategorical factorization system on the bicategory Cat of categories and functors.Each functorwhere 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.

Key concepts: Functor category, Adjoint functors, Functor, Natural transformation, Mathematics, Derived functor, Ext functor, Isomorphism (crystallography)

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