How does it integrate with existing codebases?

The skill provides specific integration patterns for Clojure using the acsets library, allowing logical models to be translated into functional code.

What is the primary purpose of the Topos Generation skill?

It is designed to generate mathematical models based on topos theory and verify logical propositions using sheaf-theoretic forcing semantics.

Can this skill be used for standard set theory?

Yes, while it supports advanced topoi like Sh(X) or Eff, it also handles classical Set theory where the subobject classifier is the standard Boolean set {0, 1}.

What is Kripke-Joyal forcing in this context?

It is a stage-wise method for determining the truth of formulas within a topos, where truth is evaluated over objects (stages) and covers rather than globally.

Topos Model Generator

Name: Topos Model Generator
Author: plurigrid

byplurigrid

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数据科学与机器学习

Generates sheaf-theoretic models and verifies logical propositions using Kripke-Joyal forcing semantics.

The Topos Generation Skill (topos-generate) provides advanced capabilities for computational category theory, specifically focused on sheaf-theoretic model generation. It allows users to construct subobject classifiers, translate formulas into the Mitchell-Bénabou internal language, and evaluate truth values via Kripke-Joyal forcing. This skill is particularly valuable for researchers and developers working on formal logic, geometric modeling, or complex system architectures requiring intuitionistic logic and stage-wise truth evaluation within a topos framework.

主要功能

01Translation of logical formulas into Mitchell-Bénabou internal language

02Automatic generation of subobject classifiers (Ω) for finite topoi

03Integration with Clojure and acsets for executable category theory models

04Support for Cohen forcing to generate new set-theoretic models

057 GitHub stars

06Kripke-Joyal forcing semantics for evaluating propositions at specific stages

使用场景

01Exploring non-classical logic and computability within the Effective Topos

02Developing formal verification models for complex software systems

03Simulating geometry and symmetry using varying sets over topological spaces

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi topos-generate

For use in Claude.ai and ChatGPT

Download Skill