Theorems · Theorem · category theory

CategoryTheory.NatTrans.naturality_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G : CategoryTheory.Functor C D} (self : CategoryTheory.NatTrans F G) ⦃X Y : C⦄ (f : X ⟶ Y) {Z : D}
  (h : G.obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.map f) (CategoryTheory.CategoryStruct.comp (self.app Y) h) =
    CategoryTheory.CategoryStruct.comp (self.app X) (CategoryTheory.CategoryStruct.comp (G.map f) h)

The naturality square for a given morphism.

Defined in

Mathlib.CategoryTheory.NatTrans

Cited by

68 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category