Categories Functors When to Use Use this skill when working on categories-functors problems in category theory. Decision Tree 1. Verify Category Axioms - Objects and morphisms (arrows) defined? - Identity morphism for each object: id A: A - A - Composition associative: (f . g) . h = f . (g . h) - Write Lean 4: 2. Check Functor Properties - F: C - D maps objects to objects, arrows to arrows - Preserves identity: F(id A) = id {F(A)} - Preserves composition: F(g . f) = F(g) . F(f) - Write Lean 4: 3. Functor Types - Covariant: preserves arrow direction - Contravariant: reverses arrow direction -…