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math-algebra-category

Organize algebraic hierarchies and categorical constructs in Lean proofs.

2|Updated May 26, 2026
Search Tags:#lean#hierarchy#algebra#formalization#type-theory#category-theory#mathlib4
One-click install
npx skills add https://github.com/r-irbe/proof-skills --skill math-algebra-category
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: math-algebra-category
Source: https://github.com/r-irbe/proof-skills/tree/main/skills/math-algebra-category
Command: npx skills add https://github.com/r-irbe/proof-skills --skill math-algebra-category

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Abstract algebra and category theory are foundational to Lean formalization; this Skill provides a structured framework to reason about algebraic hierarchies and categorical constructs.

Core Features & Use Cases

  • Domain-aligned guidance for building and navigating algebraic hierarchies (groups, rings, fields, modules) and categorical constructs (functors, natural transformations, monads) in Lean.
  • Clear handoffs to complementary skills and references for Lean math foundations, research workflows, and zettelkasten-style knowledge management.
  • Real-world scenario: formalize a simple category of monoids and a functor between categories, then verify related laws in Lean.

Quick Start

Open the math-algebra-category handbook in the references folder to begin.

Frequently Asked Questions about math-algebra-category

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

FAQPage Schema
How do I formalize algebraic hierarchies like groups and rings in Lean?▼

Formalizing algebraic hierarchies in Lean uses a structured, modular knowledge framework to organize groups, rings, fields, and modules within mathlib4 proofs.

What is the best way to reason about category theory constructs in Lean proofs?▼

Reasoning about category theory in Lean uses a structured framework to define and verify categorical constructs including categories, functors, natural transformations, and monads.

How do I build a category of monoids and verify functor laws in Lean?▼

Building a category of monoids and verifying functor laws in Lean involves following domain-aligned guidance to formalize categorical constructs and check related properties within proofs.

Does this Lean formalization framework support type-theory based mathlib4 workflows?▼

Yes, this framework supports type-theory based mathlib4 workflows by providing reusable reference materials and disciplined domain knowledge for formalization tasks.

Can I use this for organizing modules and fields in abstract algebra formalizations?▼

Yes, you can use this to organize modules and fields, as it provides specific domain-aligned guidance for navigating and building algebraic hierarchies in abstract algebra.

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