How does this skill support the 'chemputer' model?

It provides a semantic mapping where chemical species are treated as objects and chemical reactions are treated as morphisms (1-morphisms) within a Segal type.

Which formal proof assistants are compatible with this skill?

The skill includes implementation patterns and core definitions for Rzk, Lean4, and Agda, specifically utilizing the InfinityCosmos framework.

What are Segal types in this context?

In synthetic ∞-category theory, a Segal type is a type where binary composites of morphisms exist and are unique up to homotopy, serving as the foundation for categorical structure.

Why is unique composition up to homotopy important?

It ensures that the categorical structure is 'coherent,' meaning that the order of composition and associativity holds consistently across all dimensions without manual adjustment.

Segal Types Formalization

Name: Segal Types Formalization
Author: plurigrid

byplurigrid

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学习与文档

Formalizes synthetic ∞-categories using Segal types to ensure coherent composition in topological computing models.

This skill provides the logical foundation for synthetic ∞-categories within Claude Code, implementing the Riehl-Shulman (2017) framework for type theory. It enables users to define and verify Segal types where binary composites exist uniquely up to homotopy, facilitating the modeling of complex systems like topological chemputers. By bridging the gap between higher category theory and formal verification in languages like Rzk and Lean4, it ensures that compositions are coherently associative and unital at all dimensions, which is critical for verifying reaction pathways and topological interactions in advanced computational chemistry.

主要功能

01Validation of unique binary composites up to higher homotopy

02Formal definition of Segal types and directed interval types in Rzk

03Implementation of the Riehl-Shulman 2017 synthetic ∞-category framework

04Mapping of categorical morphisms to chemical reaction semantics

05Cross-language support for Lean4, Agda, and InfinityCosmos

067 GitHub stars

使用场景

01Verifying higher-dimensional categorical structures in mathematical research

02Automating proofs of coherent associativity in complex system designs

03Modeling chemical reaction networks as morphisms in a topological chemputer

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi segal-types

For use in Claude.ai and ChatGPT

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