Constructive higher sheaf models with applications to synthetic mathematics

Thierry Coquand; Jonas Höfer; Christian Sattler

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arXiv · 2605.15126

Constructive higher sheaf models with applications to synthetic mathematics

Thierry Coquand·Jonas Höfer·Christian Sattler

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Abstract

There have recently been several developments in synthetic mathematics using extensions of dependent type theory with univalence and higher inductive types: simplicial homotopy type theory, synthetic algebraic geometry and synthetic Stone duality. We provide a foundation of higher sheaf models of type theory in a constructive metatheory and, in particular, build constructive models of these formal systems.

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Thierry Coquand, Jonas Höfer, Christian Sattler. 2026-05-14. Constructive higher sheaf models with applications to synthetic mathematics. https://arxiv.org/abs/2605.15126

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