English

Universal properties of bicategories of polynomials

Category Theory 2018-12-27 v2

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.

Keywords

Cite

@article{arxiv.1806.10477,
  title  = {Universal properties of bicategories of polynomials},
  author = {Charles Walker},
  journal= {arXiv preprint arXiv:1806.10477},
  year   = {2018}
}

Comments

48 pages; final author version incorporating the suggestions of the anonymous referee; to appear in the Journal of Pure and Applied Algebra