ix-category

name	ix-category
description	Category theory primitives — monad laws verification, free-forgetful adjunction
disable-model-invocation	true

Category Theory

Verify monad laws and explore adjunctions with concrete implementations.

When to Use

When the user wants to verify monad laws, explore the Free ⊣ Forgetful adjunction, or understand category theory through executable examples.

Capabilities

• Monad laws verification — Left unit, right unit, associativity for Option/Result
• Free-Forgetful adjunction — Free functor wraps elements, Forgetful flattens back
• Round-trip verification — Forget(Free(S)) == S

Key Concepts

• Left unit: bind(unit(a), f) == f(a)
• Right unit: bind(m, unit) == m
• Associativity: bind(bind(m, f), g) == bind(m, |x| bind(f(x), g))
• Free functor: Set → Mon (wraps each element in singleton list)
• Forgetful functor: Mon → Set (flattens/concatenates)

Programmatic Usage

use ix_category::monad::{Monad, OptionMonad, ResultMonad, FreeForgetfulAdj};

MCP Tool

Tool name: ix_category Operations: monad_laws, free_forgetful