Modalities in homotopy type theory

Egbert Rijke; Michael Shulman; Bas Spitters

Modalities in homotopy type theory

Egbert Rijke, Michael Shulman, Bas Spitters

Department of Computer Science

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

26 Citations (Scopus)

Abstract

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 language	English
Journal	Logical Methods in Computer Science
Volume	16
Issue	1
Pages (from-to)	2:1-2:79
Number of pages	79
ISSN	1860-5974
Publication status	Published - 1 Jan 2020

Cite this

@article{91d13348b947478f9d460535a94d9da6,

title = "Modalities in homotopy type theory",

abstract = "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.",

author = "Egbert Rijke and Michael Shulman and Bas Spitters",

year = "2020",

month = jan,

day = "1",

language = "English",

volume = "16",

pages = "2:1--2:79",

journal = "Logical Methods in Computer Science",

issn = "1860-5974",

publisher = "International Federation for Computational Logic",

number = "1",

}

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 -

Modalities in homotopy type theory

Abstract

Other files and links

Fingerprint

Cite this