rezk-types

Name: rezk-types
Availability: InStock
Author: plurigrid

Encode local univalence in Rezk types using Lean4 and InfinityCosmos.

60|13|Updated Dec 22, 2025

Search Tags:#univalence #∞-categories #Segal #rezk

Ready to run

npx skills add https://github.com/plurigrid/asi --skill rezk-types

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: rezk-types
Source: https://github.com/plurigrid/asi/tree/main/ies/music-topos/.codex/skills/rezk-types
Command: npx skills add https://github.com/plurigrid/asi --skill rezk-types

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Rezk types encode local univalence where isomorphisms correspond to identity, providing a bridge between higher category theory and type theory.

Core Features & Use Cases

Rezk type definitions: Segal types with local univalence.
Lean4/Lua integration: Examples for integrating with Lean4 semantics.
GF(3) triads: Valid triads with segal-types.

Quick Start

Define a simple Segal-type, assert local univalence, and observe isomorphisms collapsing to identities.

Frequently Asked Questions about rezk-types

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do isomorphisms become equalities in Rezk types?▼

Rezk types encode local univalence, collapsing isomorphisms to identities within complete Segal spaces. This bridge between higher category theory and type theory lets you treat structurally equivalent objects as definitionally equal, eliminating manual conversion steps.

What are Segal types and when do I need them?▼

Segal types are higher-categorical structures where composition is weakly associative and unital. Use them when formalizing ∞-categories in type theory, particularly to model spaces where morphism composition reflects real compositional semantics rather than strict equations.

How do I work with Rezk types in Lean4?▼

Define Segal types using Lean4 semantics, assert local univalence, then construct is-iso, Iso, and id-to-iso proofs. InfinityCosmos provides the synthetic ∞-category framework; integrate Rezk completion to formalize equivalences as identities.

Can I use Rezk types without deep category theory knowledge?▼

The quick start guides you through defining a simple Segal type and observing isomorphisms collapse to identities. Core concepts—local univalence and type equivalence—are learnable incrementally, though comfort with higher-categorical intuition accelerates adoption.

What distinguishes Rezk types from other approaches to univalence?▼

Rezk types specifically target complete Segal spaces, encoding univalence locally within a type rather than globally. This scope lets you reason about isomorphisms as equalities in controlled contexts without requiring full univalent type theory.