Which programming languages are supported by this skill?

The skill provides patterns and guidance for formal verification languages including Rzk, Lean4, and Agda.

How does this relate to the concept of a 'chemputer'?

It provides a chemical interpretation where reaction products can be reasoned about by proving properties of the starting materials and propagating them through reaction pathways.

What is a Segal type in this context?

In synthetic higher category theory, a Segal type is a type that effectively behaves like a category, supporting composition and identity morphisms.

What is the primary purpose of the Directed Yoneda skill?

It facilitates directed path induction, allowing properties proven for identity morphisms to be extended to all morphisms within a Segal type.

Directed Yoneda Induction

Name: Directed Yoneda Induction
Author: plurigrid

byplurigrid

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学习与文档

Verifies and implements directed path induction for synthetic ∞-categories using the Yoneda lemma.

This skill enables Claude to apply the Riehl-Shulman insight for synthetic higher category theory (sHoTT), specifically focusing on the directed Yoneda lemma. It facilitates formal reasoning within Segal types, allowing for 'directed path induction' where properties proven at an identity morphism are automatically propagated across all reaction pathways or morphisms. This is particularly useful for researchers and developers working with Rzk, Lean4, or Agda to model complex categorical structures, chemical semantics in 'chemputers', or higher-dimensional type systems.

主要功能

01Implements directed path induction for Segal types in Rzk, Lean4, and Agda

02Validates sound induction principles within synthetic ∞-categories

037 GitHub stars

04Automates property propagation along directed reaction pathways

05Provides standardized definitions for the dependent Yoneda lemma

06Integrates chemical interpretation semantics for topological chemputer modeling

使用场景

01Formally verifying properties of morphisms in higher-dimensional categories

02Modeling chemical reaction networks using directed path induction semantics

03Developing synthetic homotopy type theory (sHoTT) proofs and library definitions

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi yoneda-directed

For use in Claude.ai and ChatGPT

Download Skill