# Modalities in homotopy type theory

@article{Rijke2019ModalitiesIH,
title={Modalities in homotopy type theory},
author={Egbert Rijke and Michael Shulman and Bas Spitters},
journal={Log. Methods Comput. Sci.},
year={2019},
volume={16}
}
• Published 2019
• Computer Science, Mathematics
• Log. Methods Comput. Sci.
• Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the theory of factorization systems, reflective subuniverses, and modalities in homotopy type theory, including their construction using a "localization" higher inductive type. This produces in particular the ($n$-connected, $n$-truncated) factorization system as… CONTINUE READING
12

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 34 CITATIONS

## Higher Structures in Homotopy Type Theory

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## The HoTT library: a formalization of homotopy type theory in Coq

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## Good Fibrations through the Modal Prism

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## Indexed type theories

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## Cartan Geometry in Modal Homotopy Type Theory

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## Semantics of higher inductive types

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• 2017

## Partial Univalence in n-truncated Type Theory

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• LICS
• 2020
VIEW 1 EXCERPT
CITES BACKGROUND

## Localization in Homotopy Type Theory

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• 2018

## Nilpotent Types and Fracture Squares in Homotopy Type Theory

VIEW 3 EXCERPTS
CITES METHODS & BACKGROUND

## On the Formalization of Higher Inductive Types and Synthetic Homotopy Theory

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2020

### CITATION STATISTICS

• 4 Highly Influenced Citations

• Averaged 9 Citations per year from 2018 through 2020

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