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Constructive Higher Sheaf Models with Applications to Synthetic Mathematics

Authors: Thierry Coquand, Jonas Höfer, and Christian Sattler

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)


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.

Cite as

Thierry Coquand, Jonas Höfer, and Christian Sattler. Constructive Higher Sheaf Models with Applications to Synthetic Mathematics. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 31:1-31:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{coquand_et_al:LIPIcs.LICS.2026.31,
  author =	{Coquand, Thierry and H\"{o}fer, Jonas and Sattler, Christian},
  title =	{{Constructive Higher Sheaf Models with Applications to Synthetic Mathematics}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{31:1--31:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.31},
  URN =		{urn:nbn:de:0030-drops-268184},
  doi =		{10.4230/LIPIcs.LICS.2026.31},
  annote =	{Keywords: Dependent type theory, homotopy type theory, univalence, models of type theory, higher sheaves, constructive mathematics, synthetic mathematics}
}
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