nLab Modalities in homotopy type theory

• Egbert Rijke, Michael Shulman, Bas Spitters:

  Modalities in homotopy type theory

  Logical Methods in Computer Science 16 1 (2020)

  arXiv:1706.07526

  lmcs:3826

on modal homotopy type theory.

Abstract. 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 well as internal presentations of subtoposes, through lex modalities. We also develop the semantics of these constructions.

See also

• Localization in Homotopy Type Theory
• homotopy type theory - references

category: reference