How does the 'chemical interpretation' work?

It treats chemical reactions as directed pathways. By proving a property for a starting material (the identity), the skill helps verify that the property holds for all potential reaction products.

What is a Segal type in this skill?

Segal types are types that possess a notion of composition, serving as the foundation for synthetic infinity-categories where directed induction is applied.

Which programming languages benefit most from this skill?

This skill is designed for formal methods and proof assistants, specifically Rzk, Lean4, and Agda.

What is the Directed Yoneda Lemma in this context?

The Directed Yoneda Lemma is treated as a directed analogue of path induction, allowing you to prove properties for all morphisms by simply proving them for the identity morphism.

Directed Yoneda Induction

Name: Directed Yoneda Induction
Author: plurigrid

byplurigrid

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개발자 도구

Implements directed path induction based on Riehl-Shulman synthetic ∞-category theory for formal verification.

This skill equips Claude with the specialized logic of the Directed Yoneda Lemma, enabling it to perform directed path induction within synthetic infinity-categories. Based on the Riehl-Shulman framework, it allows for the formal verification of properties across Segal types, specifically facilitating proofs where a property verified at the identity morphism propagates across all directed reaction pathways. It is an essential tool for developers and mathematicians working with proof assistants like Rzk, Lean4, or Agda to model non-reversible transformations, chemical semantics, and complex topological structures.

주요 기능

017 GitHub stars

02Models directed reaction pathways using chemical semantics

03Applies Riehl-Shulman synthetic ∞-category theory principles

04Supports formal proof construction in Rzk, Lean4, and Agda

05Implements directed path induction for Segal types

06Validates property propagation along morphisms from a base identity case

사용 사례

01Formally verifying non-reversible state transitions in high-integrity systems

02Proving category-theoretic properties for directed graphs and topological models

03Automating proof steps for synthetic infinity-categories in research environments

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi yoneda-directed

For use in Claude.ai and ChatGPT

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