Theorems · Theorem · category theory

CategoryTheory.conjugateEquiv_apply_app

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {L₁ L₂ : CategoryTheory.Functor C D} {R₁ R₂ : CategoryTheory.Functor D C} (adj₁ : L₁ ⊣ R₁) (adj₂ : L₂ ⊣ R₂)
  (a : L₂ ⟶ L₁) (X : D),
  ((CategoryTheory.conjugateEquiv adj₁ adj₂) a).app X =
    CategoryTheory.CategoryStruct.comp (adj₂.unit.app (R₁.obj X))
      (CategoryTheory.CategoryStruct.comp (R₂.map (a.app (R₁.obj X))) (R₂.map (adj₁.counit.app X)))

Defined in

Mathlib.CategoryTheory.Adjunction.Mates

Cited by

16 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category