Modalities in homotopy type theory

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  • Egbert Rijke, University of Ljubljana
  • ,
  • Michael Shulman, University of San Diego
  • ,
  • Bas Spitters

Univalent homotopy type theory (HoTT) may be seen as a language for the category of ∞-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.

Original languageEnglish
JournalLogical Methods in Computer Science
Volume16
Issue1
Pages (from-to)2:1-2:79
Number of pages79
ISSN1860-5974
Publication statusPublished - 1 Jan 2020

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