Does this skill help with formal verification?

Yes, it is specifically designed to verify that properties propagate correctly along morphisms in a sound, mathematical framework.

What is the directed Yoneda lemma?

The directed Yoneda lemma is a directed analogue of path induction used in synthetic infinity-category theory to prove properties about all morphisms by proving them for the identity.

What is the chemical interpretation mentioned in the skill?

It treats chemical reactions as directed pathways (morphisms), where properties of reaction products can be induced from the properties of the starting materials.

How does this skill use the Rzk language?

It provides snippets and semantic understanding for Rzk, a language designed for simplicial Homotopy Type Theory, to define Segal types and induction principles.

Directed Yoneda Lemma Reasoning

Name: Directed Yoneda Lemma Reasoning
Author: plurigrid

byplurigrid

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데이터 과학 및 ML

Implements the directed Yoneda lemma as a principle for directed path induction within synthetic infinity-categories.

This skill equips Claude with the formal machinery of the directed Yoneda lemma, as developed by Emily Riehl and Michael Shulman. It enables Claude to perform directed path induction for Segal types, allowing it to prove properties across complex reaction pathways or morphism chains by verifying only the base identity case. Ideal for researchers and developers working in synthetic homotopy type theory (sHoTT), formal verification of chemical reaction systems, and topological computing, it bridges the gap between abstract category theory and practical formal logic implementation using the Rzk language.

주요 기능

01Compositional coherence via GF(3) naturality triads

02Directed path induction for Segal types

032 GitHub stars

04Automated validation of property propagation along morphisms

05Mapping of chemical reaction pathways to category morphisms

06Rzk-lang code generation for synthetic infinity-categories

사용 사례

01Implementing directed induction principles in automated theorem proving workflows

02Modeling and validating chemical reaction networks as topological systems

03Formalizing mathematical proofs in Synthetic Homotopy Type Theory (sHoTT)

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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