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arXiv · 1806.10477

Universal properties of bicategories of polynomials

Charles Walker
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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.

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Charles Walker. 2018-06-27. Universal properties of bicategories of polynomials. https://doi.org/10.1016/j.jpaa.2018.12.004

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