Homotopy Type Theory
Univalence, higher inductive types, and synthetic homotopy theory.
Homotopy Type Theory. Univalence, higher inductive types, and synthetic homotopy theory.
Foundations and canonical references
The standard treatments of homotopy type theory approach the subject from complementary angles. Univalent-Foundations-Program, Homotopy Type Theory: Univalent Foundations of Mathematics (2013) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for homotopy type theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2013univalent-foundations-program-2013
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