How does it use DuckDB integration?

The skill queries local DuckDB databases to extract concept graphs, analyze structure dependencies, and check the status of extracted mathematical lectures.

What is the role of GF(3) trits in this skill?

It uses a ternary logic system to assign roles: -1 for foundations/constraints, 0 for transport/enrichment, and +1 for generation/extension of structures.

What mathematical levels does this skill cover?

It covers six levels ranging from Level 0 (Foundations like Sets) to Level 5 (Advanced structures like ∞-Topoi and Higher Topos Theory).

How does the gap analysis work?

It evaluates existing skills against a standard hierarchy, flagging missing areas like Bicategories or incomplete formalizations like Spivak's polynomial functors.

What is the main purpose of the cat-structure-rank skill?

It serves as a meta-coordinator that maps mathematical structures to specific Claude skills, identifying where coverage is strong and where new skills need to be developed.

Category Theory Structure Ranker

Name: Category Theory Structure Ranker
Author: plurigrid

byplurigrid

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Aprendizaje y Documentación

Maps and ranks categorical structures from sets to ∞-topoi while identifying gaps in formalization and skill coverage.

The Category Theory Structure Rank Skill serves as a navigational coordinator for high-level mathematical structures within the Claude environment. It provides a structured taxonomy ranging from basic foundations to advanced homotopical structures like ∞-topoi, integrating with DuckDB to query concept graphs and dependency maps. This skill is essential for researchers and developers working on formal methods, topological computing, or advanced AI architectures, as it performs automated gap analysis to identify missing conceptual bridges and prioritizes the creation of new specialized skills.

Características Principales

018 GitHub stars

02Automated gap analysis for identifying missing mathematical skills and formalizations

03GF(3) Trit assignment system for classifying roles as foundation, transport, or generation

04DuckDB integration for querying concept graphs and structure dependencies

05Interoperability mapping between specialized skills like ctp-yoneda and infinity-topos

06Ranked taxonomy of categorical structures across six hierarchical levels

Casos de Uso

01Coordinating a suite of specialized category theory skills for complex topological computing tasks

02Identifying missing formalization bridges in higher category theory research projects

03Querying complex mathematical dependency graphs to understand prerequisite structures

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi cat-structure-rank

For use in Claude.ai and ChatGPT

Download Skill