Homotopy Type Theory

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Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.

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2026-10-10

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1. ▲
   The Univalent Foundations Program Institute for Advanced Study. Homotopy Type Theory: Univalent Foundations of… homotopytypetheory.org

   site category #theoretical-computer-science link ↗

   The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant.

   
2. ▲
   Homotopy type theory github.com

   tool category #opensource-documents link ↗
   
3. ▲
   Homotopy Type Theory github.com

   tool category #coq link ↗

   Development of homotopy-theoretic ideas.

   
4. ▲
   Category Theory academic.oup.com

   site category #math link ↗

   Paid textbook by Steve Awodey.

5. ▲
   Category Theory in Context math.jhu.edu

   site category #math link ↗

   Emily Riehl (Johns Hopkins University).

6. ▲
   Type Theory and Functional Programming cs.kent.ac.uk

   site category #math link ↗

   Simon Thompson.

Math › Foundations and Logic > Type Theory: “Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.”