Theorems · Theorem · category theory

CategoryTheory.NatIso.naturality_2

∀ {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} {X Y : C} (α : F ≅ G) (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (α.hom.app X) (CategoryTheory.CategoryStruct.comp (G.map f) (α.inv.app Y)) =
    F.map f

Defined in

Mathlib.CategoryTheory.NatIso

Cited by

10 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category