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arXiv · 1504.05531

Homotopy-initial algebras in type theory

Steve Awodey·Nicola Gambino·Kristina Sojakova
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Abstract

We investigate inductive types in type theory, using the insights provided by homotopy type theory and univalent foundations of mathematics. We do so by introducing the new notion of a homotopy-initial algebra. This notion is defined by a purely type-theoretic contractibility condition which replaces the standard, category-theoretic universal property involving the existence and uniqueness of appropriate morphisms. Our main result characterises the types that are equivalent to W-types as homotopy-initial algebras.

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Steve Awodey, Nicola Gambino, Kristina Sojakova. 2015-04-21. Homotopy-initial algebras in type theory. https://arxiv.org/abs/1504.05531

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