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categories-functors

Verify category axioms and functor properties using Lean 4.

3.9k|296|Updated Dec 23, 2025
Search Tags:#formal verification#mathematics#abstract algebra#category theory#lean4#functors
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill categories-functors-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: categories-functors
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/category-theory/categories-functors
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill categories-functors-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes scripts (resource) and 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, ensuring adherence to mathematical axioms and functor properties.

Core Features & Use Cases

  • Axiom Verification: Guides through checking category axioms (objects, morphisms, identity, associativity).
  • Functor Property Checks: Ensures functors preserve identity and composition.
  • Functor Type Identification: Differentiates between covariant, contravariant, faithful, full, and equivalence functors.
  • Use Case: When encountering a new mathematical structure, use this skill to systematically verify if it forms a category and if a mapping between categories qualifies as a functor.

Quick Start

Use the categories-functors skill to verify the functor properties for a given mapping F.

Frequently Asked Questions about categories-functors

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

FAQPage Schema
How do I verify functor properties for a mapping in category theory?▼

To verify functor properties, you must check that the mapping preserves identity morphisms and composition. This skill guides you through systematically validating these axioms for any given functor.

What are the category axioms needed to define a mathematical structure as a category?▼

Category axioms require defining objects, morphisms, identity morphisms for each object, and ensuring associativity of composition. This skill provides strategies to systematically verify these structural requirements.

How do I differentiate between covariant, contravariant, and faithful functors?▼

Differentiating functor types involves analyzing how morphisms are mapped and if the mapping is injective or surjective. This skill helps identify covariant, contravariant, faithful, full, and equivalence functors.

Can I use Lean 4 to formally verify category theory proofs?▼

Yes, Lean 4 can be used to formally verify the mathematical definitions and proofs generated for category axioms and functor properties. This skill supports verification workflows using Lean 4.

Does this approach to category theory apply to theoretical computer science?▼

Yes, verifying category axioms and functor properties directly supports use cases in theoretical computer science and abstract algebra. It ensures mappings between mathematical structures adhere to formal definitions.

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