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categories-functors

Verify category axioms and functor properties using Lean 4 and Mathlib.

8|1|Updated Jan 4, 2026
Search Tags:#formal verification#mathlib#lean 4#mathematics#category theory#functors
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill categories-functors
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: categories-functors
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/category-theory/categories-functors
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill categories-functors

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

This skill provides a structured approach to solving problems related to categories and functors in category theory, including verification of axioms and properties.

Core Features & Use Cases

  • Axiom Verification: Check if a given structure satisfies the axioms of a category.
  • Functor Property Checking: Verify if a mapping adheres to functor properties (identity and composition preservation).
  • Lean 4 Integration: Provides guidance and commands for using Lean 4 with Mathlib for formal verification.
  • Use Case: When defining a new category or proving properties about existing ones, use this skill to ensure all conditions are met and to leverage formal verification tools.

Quick Start

Use the Lean4_Category tool to verify the category axioms for your defined structure.

Frequently Asked Questions about categories-functors

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I verify category axioms using Lean 4 and Mathlib?▼

You can verify functor properties in Lean 4 by checking if your mapping preserves identity and composition. The Skill provides specific commands and strategies for validating these functor properties within Mathlib.

What's the best way to check if a mapping preserves identity and composition for functors?▼

You need Lean 4 and Mathlib installed to perform formal verification. The Skill integrates with these tools to provide commands and guidance for checking category axioms and functor properties rigorously.

When do I need formal verification for category theory problems?▼

The Skill supports verifying common functor types and their properties, including identity and composition preservation. It provides structured verification steps for these standard functor categories within category theory.

Can I use this for proving properties about existing categories in Mathlib?▼

Yes, you can use this Skill for proving properties about existing categories in Mathlib. It provides verification steps to ensure all functor conditions are met when working with established category structures.

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