Constructive sheaf models of type theory
Artikel i vetenskaplig tidskrift, 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

Författare

Thierry Coquand

Göteborgs universitet

Fabian Ruch

Göteborgs universitet

Christian Sattler

Chalmers, Data- och informationsteknik, Datavetenskap

Mathematical Structures in Computer Science

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

Vol. 31 9 979-1002

Bevisteori och semantik för homotopitypteori i högre ordningens kategorier

Vetenskapsrådet (VR) (2019-03765), 2020-01-01 -- 2023-12-31.

Ämneskategorier

Algebra och logik

Geometri

Sannolikhetsteori och statistik

DOI

10.1017/S0960129521000359

Mer information

Senast uppdaterat

2023-11-15