Theorems · Theorem · category theory

CategoryTheory.Functor.whiskerLeft_twice

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] {B : Type u₄}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} B] (F : CategoryTheory.Functor B C) (G : CategoryTheory.Functor C D)
  {H K : CategoryTheory.Functor D E} (α : H ⟶ K),
  F.whiskerLeft (G.whiskerLeft α) =
    CategoryTheory.CategoryStruct.comp (F.associator G H).inv
      (CategoryTheory.CategoryStruct.comp ((F.comp G).whiskerLeft α) (F.associator G K).hom)

Defined in

Mathlib.CategoryTheory.Whiskering

Cited by

21 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category