Modalities in homotopy type theory

TY - JOUR

T1 - Modalities in homotopy type theory

AU - Rijke, Egbert

AU - Shulman, Michael

AU - Spitters, Bas

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85078704979&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:85078704979

SN - 1860-5974

VL - 16

SP - 2:1-2:79

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

IS - 1

ER -