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arXiv · 1802.00997

Polynomial pseudomonads and dependent type theory

Steve Awodey·Clive Newstead
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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.

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Steve Awodey, Clive Newstead. 2018-02-03. Polynomial pseudomonads and dependent type theory. https://arxiv.org/abs/1802.00997

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