Theorems · Theorem · category theory

CategoryTheory.NatTrans.naturality_inv_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} (α : F ⟶ G) {X Y : C} (f : X ⟶ Y) [inst_2 : CategoryTheory.IsIso (α.app X)]
  [inst_3 : CategoryTheory.IsIso (α.app Y)] {Z : D} (h : F.obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.inv (α.app X)) (CategoryTheory.CategoryStruct.comp (F.map f) h) =
    CategoryTheory.CategoryStruct.comp (G.map f) (CategoryTheory.CategoryStruct.comp (CategoryTheory.inv (α.app Y)) h)

Defined in

Mathlib.CategoryTheory.Functor.Category

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIsoCategoryTheory.IsIso