What is a complete Segal space?

A complete Segal space is a Segal type that satisfies the Rezk condition, serving as a fundamental model for higher category theory and homotopy theory.

Which programming languages does this skill support?

The skill provides patterns and definitions for Rzk-1, Lean4, and Ruby-based interaction entropy sequences.

How does this skill relate to chemistry?

In the chemputer model, it interprets reversible reactions at equilibrium as isomorphisms, treating them as identities to simplify chemical species classification.

Rezk Types & Local Univalence

Name: Rezk Types & Local Univalence
Author: plurigrid

byplurigrid

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데이터 과학 및 ML

Implements local univalence and complete Segal space semantics for synthetic infinity-category theory and topological chemistry.

소개

The Rezk-Types skill provides formal definitions and logical frameworks for Rezk types, where categorical isomorphisms are equivalent to type-theoretic identities. Integrating with the Rzk and Lean4 languages, it enables the modeling of 'local univalence' within synthetic infinity-categories. Specifically tailored for the 'chemputer' framework, it maps chemical equilibrium concepts to mathematical isomorphisms, allowing for rigorous reasoning about species identity, thermodynamic fixed points, and interaction entropy in complex topological systems.

주요 기능

2 GitHub stars
Rzk-1 language support for synthetic infinity-category definitions
Lean4 integration for formal verification of Rezk completions
Chemical semantics mapping for thermodynamic equilibrium modeling
GF(3) triad composition for ensuring topological coherence
Local univalence condition implementation (isomorphism equals identity)

사용 사례

Developing formal proofs in synthetic homotopy type theory (sHoTT)
Modeling chemical reaction networks where equilibrium isomers are identified as the same species
Implementing Rezk completion functors for Segal types in category theory projects

소개

주요 기능

2 GitHub stars
Rzk-1 language support for synthetic infinity-category definitions
Lean4 integration for formal verification of Rezk completions
Chemical semantics mapping for thermodynamic equilibrium modeling
GF(3) triad composition for ensuring topological coherence
Local univalence condition implementation (isomorphism equals identity)

사용 사례

Developing formal proofs in synthetic homotopy type theory (sHoTT)
Modeling chemical reaction networks where equilibrium isomers are identified as the same species
Implementing Rezk completion functors for Segal types in category theory projects