What are GF(3) triads in this context?

GF(3) triads are conservation equations that ensure naturality and compositional coherence across the skill's structural components.

What is the primary purpose of the CatSharp skill?

CatSharp serves as a home for structural properties in category theory, managing how concepts like Kan extensions compose and live within an equipment structure.

What are the 'Three Homes' defined in this skill?

The Three Homes represent the structural levels where data lives: Span (comodules), Prof (modules over spans), and Presheaves (right modules).

How does CatSharp handle data migrations?

It treats migrations as horizontal morphisms (bicomodules) in a double category, ensuring they are mathematically well-behaved and pointwise computable.

Does this skill support polynomial operations?

Yes, it includes commands to query polynomial patterns and map operations like product, parallel, and substitution to specific categorical roles.

CatSharp Categorical Coordinator

Name: CatSharp Categorical Coordinator
Author: plurigrid

byplurigrid

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Developer Tools

Orchestrates complex system structures using polynomial monoidal category theory and universal Kan extensions.

CatSharp is a specialized architectural skill for structural engineering of code and data based on Applied Category Theory (ACT). It provides a formal framework using the Cat# (polynomial comonads) definition to manage horizontal data migrations, vertical functors, and equipment structures. It is designed for developers building highly compositional systems, managing complex ACSet schemas, or implementing advanced mathematical abstractions where structural coherence and universal properties are required.

Key Features

01Polynomial Comonad (Cat#) Modeling

022 GitHub stars

03ACSet Schema Navigation and Structural Mapping

04GF(3) Triad Consistency and Naturality Checking

05Universal Kan Extension Mapping and Resolution

06Compositional Data Migration Orchestration via Bicomodules

Use Cases

01Modeling compositional system architectures using formal category theory

02Verifying structural coherence in large-scale software design patterns

03Orchestrating well-behaved data migrations between heterogeneous schemas

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi catsharp

For use in Claude.ai and ChatGPT

Download Skill