
Models of Homotopy Type Theory with an Interval Type
In this short note, we construct a class of models of an extension of ho...
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The univalence axiom in cubical sets
In this note we show that Voevodsky's univalence axiom holds in the mode...
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The Transpension Type: Technical Report
The purpose of these notes is to give a categorical semantics for the tr...
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Multimodal Dependent Type Theory
We introduce MTT, a dependent type theory which supports multiple modali...
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Internal Parametricity for Cubical Type Theory
We define a computational type theory combining the contentful equality ...
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Canonicity and normalisation for Dependent Type Theory
We show canonicity and normalization for dependent type theory with a cu...
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Transpension: The Right Adjoint to the Pitype
Presheaf models of dependent type theory have been successfully applied ...
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Presheaf Models of Relational Modalities in Dependent Type Theory
This report is an extension of 'A Model of Parametric Dependent Type Theory in Bridge/Path Cubical Sets' (Nuyts, arXiv:1706.04383). The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers (Nuyts, Vezzosi and Devriese, 2017) and with degrees of relatedness (Nuyts and Devriese, 2018).
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