# HoTT/book

A textbook on informal homotopy type theory

Repository: https://github.com/HoTT/book
Canonical: https://ross.abutalabs.com/products/hott-book
Language: TeX
License Family: other
Last push: 2026-06-18T16:22:21+00:00

## Health v2 (maintenance only)
Score: 62/100 (v2, computed 2026-09-03T02:20:16.233290+00:00)
- activity 88, release rhythm 8, longevity 100
- inputs: {"age_days": 5048, "days_push": 76, "days_rel": null, "gap_med": null, "n_releases_24m": 0}
- flags: no_license
- formula: round(0.45*activity + 0.35*rhythm + 0.20*longevity); archived -> min(score, 10)

## Adoption (not part of the score)
Stars 2167, forks 378 (observed 2026-08-28T04:06:21.435379+00:00)

## What it is
The Homotopy Type Theory book, an open-access textbook on informal homotopy type theory produced by the Univalent Foundations program at the Institute for Advanced Study. The repository contains the LaTeX source, licensed under CC BY-SA 3.0, with compiled versions distributed via the homotopytypetheory.org website.

## Use cases
- learn homotopy type theory from scratch
- study univalent foundations of mathematics
- reference the HoTT book when doing type-theoretic proofs
- find a free textbook on higher inductive types and univalence
- prepare a course on homotopy type theory
- look up definitions like equivalence, universe, and univalence axiom

## When to choose
- you want the canonical informal introduction to homotopy type theory
- you need a free, openly licensed reference on univalent foundations
- you are a mathematician or computer scientist learning type theory with a homotopical perspective

## When to avoid
- you need a formalized, machine-checked development of HoTT in a proof assistant
- you want a beginner introduction to plain type theory or programming with dependent types
- you need software or a library rather than a textbook

## Facets
- artifact type: learning-resource
- maturity: stable
- function: documentation
- domain: mathematics, education, programming-languages
- platform: cross-platform
- tags: homotopy-type-theory, univalent-foundations, textbook, tex, latex, mathematics

## Member repositories
- HoTT/book (main) score 62

## Provenance
- Observed fields: from GitHub, fetched 2026-08-28T04:06:21.435379+00:00.
- Health v2: computed from the inputs above; adoption is never an input.
- Inferred fields (summary, facets, guidance): AI-extracted, prompt v1, taxonomy v1, on 2026-08-30T02:49:31.123328+00:00, confidence not recorded.
  - readme: https://github.com/HoTT/book (fetched 2026-08-28T04:06:21.435379+00:00, sha fe4ca71cfd38)
- Data as of 2026-08-30T08:39:29.467469+00:00.