• 1 Syntax of HoTT\(0\)
  • 2 Natural Models ▶
    • 2.1 Interpretation of syntax
    • 2.2 Natural model
    • 2.3 Product types
    • 2.4 Sum types
    • 2.5 Identity types
    • 2.6 Binary products and Exponentials
    • 2.7 Univalence
    • 2.8 Extensional identity types and UIP
  • 3 HoTT\(0\) interpreted in natural models
  • 4 The Groupoid Model ▶
    • 4.1 Classifying display maps
    • 4.2 Groupoid fibrations
    • 4.3 Classifying type dependency
    • 4.4 Pi and Sigma structure
    • 4.5 Identity types
    • 4.6 Universe of Discrete Groupoids
  • 5 Polynomial Endofunctors
  • 6 Bibliography
  • Dependency graph

HoTTLean
Formalizing the Meta-Theory of HoTT in Lean

Steve Awodey Mario Carneiro Sina Hazratpour Joseph Hua Wojciech Nawrocki Spencer Woolfson

July 14, 2025

  • 1 Syntax of HoTT\(0\)
  • 2 Natural Models
    • 2.1 Interpretation of syntax
    • 2.2 Natural model
    • 2.3 Product types
    • 2.4 Sum types
    • 2.5 Identity types
    • 2.6 Binary products and Exponentials
    • 2.7 Univalence
    • 2.8 Extensional identity types and UIP
  • 3 HoTT\(0\) interpreted in natural models
  • 4 The Groupoid Model
    • 4.1 Classifying display maps
    • 4.2 Groupoid fibrations
    • 4.3 Classifying type dependency
    • 4.4 Pi and Sigma structure
    • 4.5 Identity types
    • 4.6 Universe of Discrete Groupoids
  • 5 Polynomial Endofunctors
  • 6 Bibliography