Theorems · Theorem · category theory

CategoryTheory.conjugateEquiv_whiskerLeft

∀ {A : Type u₁} {B : Type u₂} {C : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} A]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} B] [inst_2 : CategoryTheory.Category.{v₃, u₃} C]
  {L₁ L₂ : CategoryTheory.Functor B C} {R₁ R₂ : CategoryTheory.Functor C B} {L : CategoryTheory.Functor A B}
  {R : CategoryTheory.Functor B A} (adj₁ : L₁ ⊣ R₁) (adj₂ : L₂ ⊣ R₂) (adj : L ⊣ R) (τ : L₂ ⟶ L₁),
  (CategoryTheory.conjugateEquiv (adj.comp adj₁) (adj.comp adj₂)) (L.whiskerLeft τ) =
    CategoryTheory.Functor.whiskerRight ((CategoryTheory.conjugateEquiv adj₁ adj₂) τ) R

Defined in

Mathlib.CategoryTheory.Adjunction.Mates

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category