Constructive sheaf models of type theory
Journal article, 2021

We provide a constructive version of the notion of sheaf models of univalent type theory. We start by relativizing existing constructive models of univalent type theory to presheaves over a base category. Any Grothendieck topology of the base category then gives rise to a family of left-exact modalities, and we recover a model of type theory by localizing the presheaf model with respect to this family of left-exact modalities. We provide then some examples.

Dependent type theory

constructive models of univalence

left-exact modalities

homotopy type theory

sheaf models

Author

Thierry Coquand

University of Gothenburg

Fabian Ruch

University of Gothenburg

Christian Sattler

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Mathematical Structures in Computer Science

0960-1295 (ISSN) 1469-8072 (eISSN)

Vol. 31 9 979-1002

Proof theory and higher categorical semantics of homotopy type theory

Swedish Research Council (VR) (2019-03765), 2020-01-01 -- 2023-12-31.

Subject Categories

Algebra and Logic

Geometry

Probability Theory and Statistics

DOI

10.1017/S0960129521000359

More information

Latest update

11/15/2023