name: natural-transformations description: "Problem-solving strategies for natural transformations in category theory" allowed-tools: [Bash, Read]
Natural Transformations
When to Use
Use this skill when working on natural-transformations problems in category theory.
Decision Tree
-
Verify Naturality
- eta: F => G is natural transformation between functors F, G: C -> D
- For each f: A -> B in C, diagram commutes: G(f) . eta_A = eta_B . F(f)
- Write Lean 4:
theorem nat : η.app B ≫ G.map f = F.map f ≫ η.app A := η.naturality