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}
}
  • Egbert Rijke, Michael Shulman, Bas Spitters
  • 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

    Figures and Topics from this paper.

    Citations

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

    Higher Structures in Homotopy Type Theory

    VIEW 1 EXCERPT
    CITES BACKGROUND

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

    VIEW 2 EXCERPTS

    Good Fibrations through the Modal Prism

    VIEW 9 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Indexed type theories

    VIEW 3 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    Cartan Geometry in Modal Homotopy Type Theory

    VIEW 4 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Partial Univalence in n-truncated Type Theory

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Nilpotent Types and Fracture Squares in Homotopy Type Theory

    VIEW 3 EXCERPTS
    CITES METHODS & BACKGROUND

    FILTER CITATIONS BY YEAR

    2017
    2020

    CITATION STATISTICS

    • 4 Highly Influenced Citations

    • Averaged 9 Citations per year from 2018 through 2020