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arxiv 2104.02887 v1 pith:OLZ2VNZK submitted 2021-04-07 math.CT

Ross Street This is my paper · ORCID
classification math.CT
keywords functorfunctorsultimateadjointcallrightwhatbearing
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abstract

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.

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  1. On a (terminally connected, pro-etale) factorization of geometric morphisms

    math.CT 2025-02 conditional novelty 8.0 of 10

    All geometric morphisms between Grothendieck topoi admit an essentially unique (terminally connected, pro-etale) factorization, extending the classical (connected, etale) factorization.

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