What is the primary purpose of the Cat# skill?

Cat# serves as a structural coordinator that uses category theory to define how different AI capabilities and data structures compose and interact without losing logical coherence.

How does Cat# differ from standard Kan extensions?

While Kan extensions define 'what' the universal maps are, Cat# provides the 'where'—the specific equipment structure and environment where these maps live and compose.

What does 'Ergodic 0' signify in this skill?

It refers to the skill's role as a coordinator or bridge (Trit 0), sitting between consumer/limit operations (-1) and producer/colimit operations (+1) to maintain equilibrium.

What is the Three Homes Theorem in this context?

It is a classification system that maps skills into three structural structures: Spans (linear), Profunctors (bimodules), and Presheaves (right modules/cofunctors).

Can this skill help with database schema migrations?

Yes, it uses bicomodules and horizontal morphisms to manage data migrations, ensuring they are well-behaved and pointwise computable.

Cat# Polynomial Category Theory

Name: Cat# Polynomial Category Theory
Author: plurigrid

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Coordinates complex AI skill interactions using polynomial comonads and category theory principles to ensure structural coherence.

The Cat# skill provides a rigorous mathematical framework for Claude Code, implementing David Spivak’s 'All Concepts are Cat#' thesis. It acts as a meta-coordinator that organizes skills into a polynomial monoidal category, managing them as bicomodules to ensure compositional integrity. By leveraging the 'Three Homes Theorem' (Span, Prof, and Presheaves), it provides a structured environment for Kan extensions, data migrations, and equipment structure, making it indispensable for developers building deeply integrated, modular AI systems that require formal logical consistency.

主な機能

01Kan extension bridging for universal property resolution (Lan/Ran)

028 GitHub stars

03Polynomial comonad modeling for advanced skill orchestration

04Automated mapping of system behaviors to Span, Prof, and Presheaf structures

05GF(3) triad balancing to maintain naturality and compositional coherence

06Queryable database views for polynomial patterns and ACSet schema navigation

ユースケース

01Ensuring structural integrity across large-scale multi-agent AI architectures

02Verifying the mathematical consistency of modular software components

03Managing complex data migrations and profunctor-based transformations

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