Constructive sheaf models of type theory-Reference-Cited by-同舟云学术

Constructive sheaf models of type theory

Published:2021-11-18 Issue: Volume: Page:1-24
ISSN:0960-1295
Container-title:Mathematical Structures in Computer Science
language:en
Short-container-title:Math. Struct. Comp. Sci.

Author:

Coquand Thierry^ORCID,Ruch Fabian,Sattler Christian^ORCID

Abstract

Abstract 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.

Publisher

Cambridge University Press (CUP)

Subject

Computer Science Applications,Mathematics (miscellaneous)

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