rezk-types
Rezk types (complete Segal spaces). Local univalence: categorical isomorphisms ≃ type-theoretic identities.
Profile →npx skills add majiayu000/claude-skill-registry --skill rezk-types --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Rezk Types Skill > *"In a Rezk type, isomorphisms are equivalent to identities — local univalence."* > — Emily Riehl & Michael Shulman ## Overview Rezk types are Segal types with an additional **local univalence** condition: categorical isomorphisms are equivalent to type-theoretic identities. This is the ∞-categorical analogue of the univalence axiom. ## Core Definitions (Rzk) ```rzk #lang rzk-1 -- Isomorphism in a Segal type #define is-iso (A : Segal) (x y : A) (f : hom A x y) : U := Σ (g : hom A y x), (hom2 A x y x f g (id x)) × (hom2 A y x y g f (id y)) -- The type of isomorphisms #define Iso (A : Segal) (x y : A) : U := Σ (f : hom A x y), is-iso A x y f -- Identity-to-isomorphism map #define id-to-iso (A : Segal) (x y : A) : (x = y) → Iso A x y := λ p. transport (λ z. Iso A x z) p (id x, refl-iso) -- Rezk condition (local univalence) #define is-rezk (A : Segal) : U := (x y : A) → is-equiv (id-to-iso A x y) -- Rezk type (complete Segal space) #define Rezk : U := Σ (A : Segal), is-rezk A ``` ## Chemputer Semantics | ∞-Category Concept | Chemical Interpretation | |--------------------|------------------------| | Isomorphism | Reversible reaction (equilibrium) | | Local univalen
- Overview
- Core Definitions (Rzk)
- Chemputer Semantics
- GF(3) Triad
- The Local Univalence Principle
- Lean4 Integration
- Integration with Interaction Entropy
- Key Theorems
- References
- Scientific Skill Interleaving
- Graph Theory
- Bibliography References
- SDF Interleaving
- Primary Chapter: 3. Variations on an Arithmetic Theme
What does the rezk-types skill do?
Rezk types (complete Segal spaces). Local univalence: categorical isomorphisms ≃ type-theoretic identities.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill rezk-types --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.