Homotopy Type Theory

Univalence, higher inductive types, and synthetic homotopy theory.


frontier tier

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

In context

Where this topic sits in the prerequisite graph. Click any node to jump.

Open in full atlas →


Review this topic

This page was drafted by an agent and is waiting on expert review. Spotted a wrong prerequisite, a missing concept, a misattributed source, or a factual slip? Tell us — your review opens a tracked issue maintainers act on.