Constructive sheaf models of type theory

Thierry Coquand; Fabian Ruch; Christian Sattler

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arXiv · 1912.10407

Constructive sheaf models of type theory

Thierry Coquand·Fabian Ruch·Christian Sattler

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Abstract

We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any presheaf models, and these sheaf models are obtained by localisation for a left exact modality. We provide first an abstract notion of descent data which can be thought of as a higher version of the notion of prenucleus on frames, from which can be generated a nucleus (left exact modality) by transfinite iteration. We then provide several examples.

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BibTeX RIS

Thierry Coquand, Fabian Ruch, Christian Sattler. 2019-12-22. Constructive sheaf models of type theory. https://arxiv.org/abs/1912.10407

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