Homotopy Type Theory
Modalities in homotopy type theory (changes)

Showing changes from revision #2 to #3: Added | Removed | Changed

Modalities in homotopy type theory. Egbert Rijke, Michael Shulman, Bas Spitters.



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 (nn-connected, nn-truncated) factorization system as well as internal presentations of subtoposes, through lex modalities. We also develop the semantics of these constructions.

See also

category: reference

Last revised on January 19, 2019 at 13:06:09. See the history of this page for a list of all contributions to it.