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 language | English |
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Pages (from-to) | 3722-3777 |
Number of pages | 56 |
Journal | Journal of Pure and Applied Algebra |
Volume | 223 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sept 2019 |
Keywords
- Polynomial functors