javra / cubes

Cubcial sets in Lean.

A Formalization of Cubical Sets in Lean

Preliminaries:

• fi: The inductive family of finite ordinal types

Basics of cubical sets:

• cubes: The cube category for arbitrary name systems
• cubes_list: The cube category for lists
• cubes_fin: The cube category for finite types
• cset: Declaration of cubical sets
• kan: The uniform Kan condition on cubical sets

Constructions on Kan cubical sets:

• sigma: Kan cubical sets model sigma types
• pi: Kan cubical sets model pi types

These constructions are loosely based on Simon Huber's version of cubical sets as a model for Homotopy Type Theory, which you can find online.