English

Polynomial pseudomonads and dependent type theory

Category Theory 2018-02-06 v1 Logic

Abstract

We assemble polynomials in a locally cartesian closed category into a tricategory, allowing us to define the notion of a polynomial pseudomonad and polynomial pseudoalgebra. Working in the context of natural models of type theory, we prove that dependent type theories admitting a unit type and dependent sum types give rise to polynomial pseudomonads, and that those admitting dependent product types give rise to polynomial pseudoalgebras.

Keywords

Cite

@article{arxiv.1802.00997,
  title  = {Polynomial pseudomonads and dependent type theory},
  author = {Steve Awodey and Clive Newstead},
  journal= {arXiv preprint arXiv:1802.00997},
  year   = {2018}
}

Comments

26 pages

R2 v1 2026-06-23T00:09:45.177Z