Constructive Higher Sheaf Models with Applications to Synthetic Mathematics
Paper in proceeding, 2026
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.
Dependent type theory
univalence
higher sheaves
synthetic mathematics
homotopy type theory
models of type theory
constructive mathematics
Author
Thierry Coquand
University of Gothenburg
Chalmers, Computer Science and Engineering (Chalmers), Computing Science
Jonas Höfer
University of Gothenburg
Chalmers, Computer Science and Engineering (Chalmers), Computing Science
Christian Sattler
University of Gothenburg
Chalmers, Computer Science and Engineering (Chalmers), Computing Science
Leibniz International Proceedings in Informatics, LIPIcs
18688969 (ISSN)
Vol. 380 319783959774345 (ISBN)
41st Annual Symposium on Logic in Computer Science, LICS 2026
Lisbon, Portugal,
Lisbon, Portugal,
Subject Categories (SSIF 2025)
Algebra and Logic
DOI
10.4230/LIPIcs.LICS.2026.31