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Polynomial pseudomonads and dependent type theory

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arxiv 1802.00997 v1 pith:2AZ63TFO submitted 2018-02-03 math.CT math.LO

Steve Awodey , Clive Newstead This is my paper · ORCID
classification math.CTmath.LO
keywords polynomialdependenttypeadmittinggivepseudomonadsrisetheory
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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.

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Cited by 1 Pith paper

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  1. Algebraic Type Theory, Part 1: Martin-L\"of algebras

    math.CT 2025-05 conditional novelty 6.0 of 10

    Introduces Martin-Löf algebras as algebraic models of dependent type theory and constructs a bicategory E//U in which the type former laws become pseudomonoid laws.

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