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arXiv · 1806.08490

Cubical informal type theory: the higher groupoid structure

Bruno Bentzen
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Abstract

Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing higher-dimensional constructions via Voevodsky's univalance axiom and higher-inductive types, this paper proposes a way of doing informal type theory with a cubical type theory as the underlying foundation instead. To that end, we adopt a cubical type theory recently proposed by Angiuli, Hou (Favonia) and Harper, a framework with a cumulative hierarchy of univalent Kan universes, full univalence and instances of higher-inductive types. In the present paper we confine ourselves to some elementary theorems concerning the higher groupoid structure of types.

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Bruno Bentzen. 2018-06-22. Cubical informal type theory: the higher groupoid structure. https://arxiv.org/abs/1806.08490

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