Universal properties of bicategories of polynomials

Charles Walker

    Research output: Contribution to journalArticle

    Abstract

    We establish the universal properties of the bicategory of polynomials, considering both cartesian and general morphisms between these polynomials. A direct proof of these universal properties would be impractical due to the complicated coherence conditions arising from polynomial composition; however, in this paper we avoid most of these coherence conditions using the properties of generic bicategories. In addition, we give a new proof of the universal properties of the bicategory of spans, and also establish the universal properties of the bicategory of spans with invertible 2-cells; showing how these properties may be used to describe the universal properties of polynomials.

    Original languageEnglish
    Pages (from-to)3722-3777
    Number of pages56
    JournalJournal of Pure and Applied Algebra
    Volume223
    Issue number9
    DOIs
    Publication statusPublished - Sep 2019

    Keywords

    • Polynomial functors

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